The Idea in Brief
Haman appears to have built the wooden scaffolding for two reasons: one, the hanging on wood would represent Mordecai as a cursed man in Jewish Law (Deut 21:22); and secondly, the timing of Mordecai's hanging in addition to the height of the sacaffolding appear to correspond to the "50" days after the Passover, which was the point when Haman had originally issued the edict to kill the Jews under the authority of the king. In other words, Mordecai's hanging "50" days later on a wooden scaffolding "50" cubits high would not only have humiliated and destroyed Mordecai the Jew, but was a portent of what was coming for the Jewish people later that year. So the death of Mordecai was to be the "first fruits" of what was to come for all Jews. That is, the moment was not to be the time of gladness and celebration (Feast of Weeks/Festival of First Fruits), but a time of death and sorrow.
Under the authority of the king, Haman issued the surprise proclamation on the eve of Passover to kill the Jews (Esther 3:12). That is, on the eve of Passover the scribes of the king issued the proclamation, which then went out to every province of the kingdom. At a subsequent point from that proclamation, Haman complained to his wife and friends concerning the Jew Mordecai. Their suggestion was to build the scaffolding of wood, which was 50 cubits high (Esther 5:14). Haman fabricated the wood scaffolding that same day, since his intent was to hang Mordecai the following morning. By hanging him on a tree (something constructed of wood) the message in Jewish eyes was that Mordecai was a cursed man (Deut 21:22).
At the critical juncture in the text, Esther invoked three days of fasting and mourning in anticipation of her engagement with the king, which, if rejected, would have resulted in her own execution (Esther 4:15-16). In other words, over the next three days, Esther cancelled any festivities in observance with Shavuot (Feast of Weeks/Festival of First Fruits).
THEREFORE IF that following day, when Mordecai was to be hanged, was Shuvuot (6 Sivan), then it was Haman who had enabled Mordecai to celebrate that day with gladness and celebration, since Haman had paraded Mordecai in the city square, who was mounted on a horse dressed in the king's robes. The following passages indicate that this day of Shuvuot (Feast of Weeks/Festival of First Fruits) was one of gladness and celebration and honor.
Deuteronomy 16:10-11 (NASB)
10 Then you shall celebrate the Feast of Weeks to the Lord your God with a tribute of a freewill offering of your hand, which you shall give just as the Lord your God blesses you; 11 and you shall rejoice before the Lord your God, you and your son and your daughter and your male and female servants and the Levite who is in your town, and the stranger and the orphan and the widow who are in your midst, in the place where the Lord your God chooses to establish His name.
This gladness and celebration coincides with the honor promised by Yahveh on Shavuot, which was the Festival of First Fruits (Feast of Weeks) - that is, the following verses in Deuteronomy concerns Shavuot, and the resultant honor in the eyes of the nations, who were the enemies of the Jews.
Deuteronomy 26:16-19 (NASB)
16 “This day the Lord your God commands you to do these statutes and ordinances. You shall therefore be careful to do them with all your heart and with all your soul. 17 You have today declared the Lord to be your God, and that you would walk in His ways and keep His statutes, His commandments and His ordinances, and listen to His voice. 18 The Lord has today declared you to be His people, a treasured possession, as He promised you, and that you should keep all His commandments; 19 and that He will set you high above all nations which He has made, for praise, fame, and honor; and that you shall be a consecrated people to the Lord your God, as He has spoken.”
When Haman's wife and friends heard that Haman was forced to honor Mordecai in the city square mounted on the king's horse dressed in the king's clothes, their response was as follows.
Esther 6:13 (NASB)
13 Haman recounted to Zeresh his wife and all his friends everything that had happened to him. Then his wise men and Zeresh his wife said to him, “If Mordecai, before whom you have begun to fall, is of Jewish origin, you will not overcome him, but will surely fall before him.”
These Gentiles not only had some familiarization with the Jewish calendar and Jewish Law, but knew that these Jews were servants of the Living God, who would fight on their behalf. This honor of Mordecai by Haman was therefore the ominous portent of the demise of the House of Haman in the eyes of his wife and "wise men."
As the narrative continues, Haman is hanged, and Mordecai takes his position. Mordecai then countermanded the decree of Haman with another decree by the king.
Esther 8:9 (NASB)
9 So the king’s scribes were called at that time in the third month (that is, the month Sivan), on the twenty-third day; and it was written according to all that Mordecai commanded to the Jews, the satraps, the governors and the princes of the provinces which extended from India to Ethiopia, 127 provinces, to every province according to its script, and to every people according to their language as well as to the Jews according to their script and their language.
The point here is that the Feast of Weeks (or Festival of First Fruits) was on the 6th of that month, which was two weeks and two days earlier. In other words, this countermand by Mordecai occurred a short time after the showdown with Haman, who was hanged on his own scaffolding. The text does not indicate the amount of time that had transpired from the hanging and the countermand decree issued by Mordecai. Therefore IF the hanging occurred on the 6th of Sivan (as we assume), THEN the timing of both the decree to kill the Jews (Passover) and the intent to kill Mordecai (Shuvuot) coincided with these two respective Jewish Holy Days associated with deliverance from their enemies and prosperity at the hand of Yahveh, which is the meta-narrative of the Book of Esther.
Consistent with all the events of the Book of Esther, the "50" cubits height of the wooden scaffolding therefore would have been the coincidental parallel to the "50" days of Shuvuot (Feast of Weeks/Festival of First Fruits). On the other hand, as the Book of Esther demonstrates, there was nothing that had happened in the story that was coincidental.