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• Simple spatial completeness (which is usually four):
  • in one dimension (east/west in 8:7 and 14:8; north/south in 6:6, where "the four winds of heaven" were just mentioned in verse 5, and yet east/west are not mentioned; going out/coming in in 8:10; going/marching to and fro in 7:14 and 9:8)
  • in two dimensions (width/length in 2:2 and 5:2; sea to sea in 9:10 and 14:8)
• Simple temporal completeness (day/night in 14:7; winter/summer in 14:8; year after year in 14:16; seems to carry the idea of eternity)
• Rhetorical emphasis:

  • Simple repetition: Direct and strong, almost sharp (2:6; 4:7)

  • Repetitious parallelism: strong but not as abrupt; e.g. 8:10—

    For before those days there was no wage for man or wage for beast. (ESV)

    and gloriously (I can't read this without Handel's Messiah in my head):

    Rejoice greatly, O daughter of Zion!
    Shout aloud, O daughter of Jerusalem!
    Behold, your king is coming to you;
    righteous and having salvation is he,
    humble and mounted on a donkey,
    on a colt, the foal of a donkey. —9:9

    And with a little different twist:

    As I called, and they would not hear, so they called, and I would not hear. —7:13

  • Parallelism: more subtle; e.g. 13:1—

    On that day there shall be a fountain opened for the house of David and the inhabitants of Jerusalem to cleanse them from sin and uncleanness.

• Traditional pairs which are common in Scripture and human culture ("parallelism" might be classified here as well):
  • Tyre and Sidon (9:2), possibly a form of localized geographical completeness, as it is part of a passage which seems to be given to geographical completeness—note Ashkelon, Gaza and Ekron in 9:5
  • Silver and gold (9:3), standing for all kinds of wealth (see also 6:11 and 13:9, where they probably don't bear synecdochic completeness)
• Two of the offices of the Messiah, priest and king, with the third being hidden by virtue of proximity in the person of the prophet (thus the olive trees, branches, golden pipes, anointed ones, Yeshua and Zerubbabel)
• Division/destruction
  • In chapter 11, there are the two staffs of Zechariah, Favor and Union, and each are broken in two. The breaking of union annuls the brotherhood between Israel and Judah.
  • Two thirds of the people will be cut off and perish (13:8). Similarly, in 14:2, the city is divided into two parts: those who will go into exile, and those who will be left behind and blessed.

• Simple spatial completeness (which is usually four):
  • in one dimension (east/west in 8:7 and 14:8; north/south in 6:6, where "the four winds of heaven" were just mentioned in verse 5, and yet east/west are not mentioned; going out/coming in in 8:10; going/marching to and fro in 7:14 and 9:8)
  • in two dimensions (width/length in 2:2 and 5:2; sea to sea in 9:10 and 14:8)
• Simple temporal completeness (day/night in 14:7; winter/summer in 14:8; year after year in 14:16; seems to carry the idea of eternity)
• Rhetorical emphasis:

  • Simple repetition: Direct and strong, almost sharp (2:6; 4:7)

  • Repetitious parallelism: strong but not as abrupt; e.g. 8:10—

    For before those days there was no wage for man or wage for beast. (ESV)

    and gloriously (I can't read this without Handel's Messiah in my head):

    Rejoice greatly, O daughter of Zion!
    Shout aloud, O daughter of Jerusalem!
    Behold, your king is coming to you;
    righteous and having salvation is he,
    humble and mounted on a donkey,
    on a colt, the foal of a donkey. —9:9

    And with a little different twist:

    As I called, and they would not hear, so they called, and I would not hear. —7:13

  • Parallelism: more subtle; e.g. 13:1—

    On that day there shall be a fountain opened for the house of David and the inhabitants of Jerusalem to cleanse them from sin and uncleanness.

• Traditional pairs which are common in Scripture and human culture ("parallelism" might be classified here as well):
  • Tyre and Sidon (9:2), possibly a form of localized geographical completeness, as it is part of a passage which seems to be given to geographical completeness—note Ashkelon, Gaza and Ekron in 9:5
  • Silver and gold (9:3), standing for all kinds of wealth (see also 6:11 and 13:9, where they probably don't bear synecdochic completeness)
• Two of the offices of the Messiah, priest and king, with the third being hidden by virtue of proximity in the person of the prophet (thus the olive trees, branches, golden pipes, anointed ones, Yeshua and Zerubbabel)
• Division/destruction
  • In chapter 11, there are the two staffs of Zechariah, Favor and Union, and each are broken in two. The breaking of union annuls the brotherhood between Israel and Judah.
  • Two thirds of the people will be cut off and perish (13:8). Similarly, in 14:2, the city is divided into two parts: those who will go into exile, and those who will be left behind and blessed.

• Simple spatial completeness (which is usually four):
  • in one dimension (east/west in 8:7 and 14:8; north/south in 6:6, where "the four winds of heaven" were just mentioned in verse 5, and yet east/west are not mentioned; going out/coming in in 8:10; marching to and fro in 9:8)
  • in two dimensions (width/length in 2:2 and 5:2; sea to sea in 9:10)
• Simple temporal completeness (day/night in 14:7; winter/summer in 14:8; seems to carry the idea of eternity)
• Rhetorical emphasis:

  • Simple repetition: Direct and strong, almost sharp (2:6; 4:7)

  • Repetitious parallelism: strong but not as abrupt; e.g. 8:10—

    For before those days there was no wage for man or wage for beast. (ESV)

    and gloriously (I can't read this without Handel's Messiah in my head):

    Rejoice greatly, O daughter of Zion!
    Shout aloud, O daughter of Jerusalem!
    Behold, your king is coming to you;
    righteous and having salvation is he,
    humble and mounted on a donkey,
    on a colt, the foal of a donkey. —9:9

  • Parallelism: more subtle; e.g. 13:1—

    On that day there shall be a fountain opened for the house of David and the inhabitants of Jerusalem to cleanse them from sin and uncleanness.

• Traditional pairs which are common in Scripture and human culture ("parallelism" might be classified here as well):
  • Tyre and Sidon (9:2), possibly a form of localized geographical completeness, as it is part of a passage which seems to be given to geographical completeness—note Ashkelon, Gaza and Ekron in 9:5
  • Silver and gold (9:3), standing for all kinds of wealth
• Two of the offices of the Messiah, priest and king, with the third being hidden by virtue of proximity in the person of the prophet (thus the olive trees, branches, golden pipes, anointed ones, Yeshua and Zerubbabel)

• Simple spatial completeness (which is usually four):
  • in one dimension (east/west in 8:7 and 14:8; north/south in 6:6, where "the four winds of heaven" were just mentioned in verse 5, and yet east/west are not mentioned; going out/coming in in 8:10; going/marching to and fro in 7:14 and 9:8)
  • in two dimensions (width/length in 2:2 and 5:2; sea to sea in 9:10 and 14:8)
• Simple temporal completeness (day/night in 14:7; winter/summer in 14:8; year after year in 14:16; seems to carry the idea of eternity)
• Rhetorical emphasis:

  • Simple repetition: Direct and strong, almost sharp (2:6; 4:7)

  • Repetitious parallelism: strong but not as abrupt; e.g. 8:10—

    For before those days there was no wage for man or wage for beast. (ESV)

    and gloriously (I can't read this without Handel's Messiah in my head):

    Rejoice greatly, O daughter of Zion!
    Shout aloud, O daughter of Jerusalem!
    Behold, your king is coming to you;
    righteous and having salvation is he,
    humble and mounted on a donkey,
    on a colt, the foal of a donkey. —9:9

    And with a little different twist:

    As I called, and they would not hear, so they called, and I would not hear. —7:13

  • Parallelism: more subtle; e.g. 13:1—

    On that day there shall be a fountain opened for the house of David and the inhabitants of Jerusalem to cleanse them from sin and uncleanness.

• Traditional pairs which are common in Scripture and human culture ("parallelism" might be classified here as well):
  • Tyre and Sidon (9:2), possibly a form of localized geographical completeness, as it is part of a passage which seems to be given to geographical completeness—note Ashkelon, Gaza and Ekron in 9:5
  • Silver and gold (9:3), standing for all kinds of wealth (see also 6:11 and 13:9, where they probably don't bear synecdochic completeness)
• Two of the offices of the Messiah, priest and king, with the third being hidden by virtue of proximity in the person of the prophet (thus the olive trees, branches, golden pipes, anointed ones, Yeshua and Zerubbabel)
• Division/destruction
  • In chapter 11, there are the two staffs of Zechariah, Favor and Union, and each are broken in two. The breaking of union annuls the brotherhood between Israel and Judah.
  • Two thirds of the people will be cut off and perish (13:8). Similarly, in 14:2, the city is divided into two parts: those who will go into exile, and those who will be left behind and blessed.

After considering the other answers, I have some thoughts to add. These are to be taken as suggestions rather than conclusions.

• Simple spatial completeness (which is usually four):
  • in one dimension (east/west in 14:8; north/south in 6:6, where "the four winds of heaven" were just mentioned in verse 5, and yet east/west are not mentioned); this could also be classified under binary completeness (completeness in any case of simple opposites)
  • in two dimensions (width/length in 2:2 and 5:2) Two angels in chapters 1 and 2
• Simple temporal completeness (day/night in 14:7; winter/summer in 14:8; seems to carry the idea of eternity)
• Rhetorical emphasis:
  • Repetition: Direct and strong (2:6; 4:7)
  • Parallelism: more subtle; e.g. 13:1—

    On that day there shall be a fountain opened for the house of David and the inhabitants of Jerusalem to cleanse them from sin and uncleanness. (ESV)

• Two of the offices of the Messiah, priest and king, with the third being hidden by virtue of proximity in the person of the prophet (thus the olive trees, branches, golden pipes, anointed ones, Yeshua and Zerubbabel)

That explains some of the individual cases; but is there any unifying reason why Zechariah, under the power of the Spirit of God, uses the number two? Some guesses:

This answer is not yet fully satisfactory to me.

The Totality of Two

Jon Ericson claimed in his answer that two may be a number of completeness. At first I found this surprising, but I begin to find myself persuaded; and because technical terms have a power of persuasion in themselves, I have called it binary completeness. One may think of two sides of a coin, or two people in a marriage, or any number of things listed below. Also, if you have a bow but no arrow you have an incomplete weapon (see 9:13).

Two could also have what might be called synecdochic completeness, in which two significant parts are offered as a representative sampling of a whole. (This is a common function of parallelism.) "Tyre and Sidon" may function this way; I think "silver and gold" do. However, three or four might function equally well for this type of completeness.

The Taxonomy of Two

I have found it helpful to organize the types of occurrences of the number. This is not a complete analysis.

• Simple spatial completeness (which is usually four):
  • in one dimension (east/west in 8:7 and 14:8; north/south in 6:6, where "the four winds of heaven" were just mentioned in verse 5, and yet east/west are not mentioned; going out/coming in in 8:10; marching to and fro in 9:8)
  • in two dimensions (width/length in 2:2 and 5:2; sea to sea in 9:10)
• Simple temporal completeness (day/night in 14:7; winter/summer in 14:8; seems to carry the idea of eternity)
• Rhetorical emphasis:

  • Simple repetition: Direct and strong, almost sharp (2:6; 4:7)

  • Repetitious parallelism: strong but not as abrupt; e.g. 8:10—

    For before those days there was no wage for man or wage for beast. (ESV)

    and gloriously (I can't read this without Handel's Messiah in my head):

    Rejoice greatly, O daughter of Zion!
    Shout aloud, O daughter of Jerusalem!
    Behold, your king is coming to you;
    righteous and having salvation is he,
    humble and mounted on a donkey,
    on a colt, the foal of a donkey. —9:9

  • Parallelism: more subtle; e.g. 13:1—

    On that day there shall be a fountain opened for the house of David and the inhabitants of Jerusalem to cleanse them from sin and uncleanness.

• Traditional pairs which are common in Scripture and human culture ("parallelism" might be classified here as well):
  • Tyre and Sidon (9:2), possibly a form of localized geographical completeness, as it is part of a passage which seems to be given to geographical completeness—note Ashkelon, Gaza and Ekron in 9:5
  • Silver and gold (9:3), standing for all kinds of wealth
• Two of the offices of the Messiah, priest and king, with the third being hidden by virtue of proximity in the person of the prophet (thus the olive trees, branches, golden pipes, anointed ones, Yeshua and Zerubbabel)

Two as a Theme

That explains some of the individual cases; but is there any unifying reason why Zechariah, under the power of the Spirit of God, uses the number two? I have concluded there is no single, exclusive theological meaning of the number in the book. Nevertheless, I can guess at some literary reasons which have theological overtones: