The more one researches this the more questions arise rather than answers. At the very least the root ילל has at least equal possibility with the root הלל. However, tradition favors הלל. This is the position that the Septuagint (LXX) translators took. The LXX was the Old Testament used by the early Church, thus forming traditions. If Gesenius's statement about Jerome's view (ילל) of Isaiah 14:12 is correct, Christian leaders must have talked him into the traditional (הלל) lucifer in the Vulgate. Then, some argue for a parallel (to הלל) in Ugaritic literature. The root ילל has the advantage that it fits the imperative form which fits the context. (I would tend toward the root ילל as the best answer.) However, the root הלל makes הֵילֵ֣ל a noun with a meaning that is also possible. Both roots have people endorsing very early, and we are too far removed to tell. Greek has a huge amount of literature outside the New Testament, but we do not have this luxury with the Hebrew of the Old Testament.
Isaiah 14:12 even in the JPS Tanakh is translated:
How are you fallen from heaven,
O Shining One, son of Dawn!
How are you felled to earth,
O vanquisher of nations!
If you take root to be ילל, it would be "howling/wailing one" instead of "Shining One." In Jeremiah 47:2, Zechariah 11:2, and Ezekiel 21:12 the forms are verbs, not nouns. Jeremiah 47:2 and Ezekiel 21:12 have the waw consecutive (וְהֵילִ֕ל). Only Zechariah 11:2 is exactly the same in letters including vowel points, and it is an imperative, which isn't used as a noun. The Septuagint translates it ὁ ἑωσφόρος (morning, morning star). To be accurate, you would need to translate this as an imperative verb "Wail, son of Dawn." Who translates הֵילֵ֣ל in Isaiah 14:12 "howling/wailing?"
Micah answered this question, "Aquila in the 2nd century AD to Greek." The root ילל does also fit the context and could be translated.
How are you fallen from heaven,
Wail, son of Dawn!
How are you felled to earth,
O vanquisher of nations!
Like Zechariah 11:2 translated by JPS.
Wail [הֵילֵ֤ל], O cypress, for the cedar has fallen,
for the glorious trees are ruined!
Wail [הֵילִ֨ילוּ֙, plural], oaks of Bashan,
for the thick forest has been felled!
However, what is hard to explain is why we don't find Jews translating הֵילֵ֣ל in Isaiah 14:12 as from the root ילל. It's not because the Latin Vulgate translates הֵילֵ֤ל as lucifer which means light-bringing, morning star, not a proper name. At least an Orthodox Jew told me they don't believe the devil is a real being.
Lexicon
הֵילֵל Isa. 14:12 according to LXX., Vulg., Targ. Rabbin. Luth., stella lucida, bright star, i.e. Lucifer. Nor is this a bad rendering, for there is added בֶּן־שַׁחַר and in the Chaldee also Lucifer [the morning star], is called כּוֹכַב נָגְהָה, in Arab. زُهَرَةُ i.e. splendid star. According to this opinion הֵילֵל would be derived from the root הלל to shine; as a participial noun of the conj. קֵיטֵל, (comp. Arab. بَيْطَرَ, Syr. ܣܰܝܒܰܪ and the like), or else of a quadriliteral verb הילל, comp. הֵיכָל, הֵידָד. However, הֵילֵל itself is not unfrequently Imper. Hiph. of the verb יָלַל in the signification wail, lament (Eze. 21:17; Zec. 11:2), and this does not appear less suitable, and is adopted by Syr., Aqu. and Jerome. [“This is less suitable.” Ges. corr.]
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Gesenius, W., & Tregelles, S. P. (2003). In Gesenius’ Hebrew and Chaldee lexicon to the Old Testament Scriptures (pp. 222–223). Logos Bible Software.
Commentaries
Shining and high was he once, like the morning star; now he is fallen from heaven. הֵילֵל, shining star, is called “son of the morning,” because it seems to emerge out of the morning dawn (comes et alumnus aurorae). “In the southern heavens, when mirrored in the waves of the sea, this planet has a brighter gleam than with us” (LEYRER in HERZ.R. Encycl. XIX. p. 563). TERTULLIAN, GREGORY THE GREAT, and latterly STIER, with reference to Luke 10:18, have taken the star fallen from heaven for Satan.
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Lange, J. P., Schaff, P., Nägelsbach, C. W. E., Lowrie, S. T., & Moore, D. (2008). A commentary on the Holy Scriptures: Isaiah (p. 187). Logos Bible Software.
Commentary supporting הלל with the root, sighting connection to Ugarit literature.
O morning star, son of the dawn: The king is identified with a mythological figure from Canaanite religion. From the Ugaritic texts we know of Shahar, the god of “dawn” (šāḥar); his son is the “morning star” (hēlāl), giving us the mythical Helal ben Shahar. The Vg translates “morning star” as “Lucifer.” Some fathers of the Church have applied this verse to the fall of Satan, prince of demons.13. The entire verse swarms with Canaanite imagery, now familiar from the Ugaritic literature (VBW 3, 39). The writer has used an ancient Canaanite myth about a lesser god’s attempt to become head of the pantheon to illustrate the pride of an earthly king. The mount of assembly refers to a sacred mountain on the N Syrian coast; it was called Mt. Caseus and today is known as Jebel Aqra.
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Brown, R. E., Fitzmyer, J. A., & Murphy, R. E. (1996). The Jerome Biblical commentary (Vol. 1, p. 274). Prentice-Hall.
A counter to the Ugaritic connection is at the link: https://digitalcommons.liberty.edu/cgi/viewcontent.cgi?article=1279&context=lts_fac_pubs
Abstract: Many scholars of the Hebrew Bible have postulated that the source of the taunt-song of Isa xiv 12-15 is to be found in Ugaritic religious literature Many of these scholars believe that the passage contains elements of both El and Baal myths, an assumption that leads them to discount the proposition that all the mythological strands of Isa xiv 12-15 can be correlated with a single Ugaritic myth Still others contend that only a single myth concerning the usurpation of El can account for all of the mythological features This article disputes both of these positions, arguing that no usurpation of El is in view, and that the mythological provenance of Isa xiv 12-15 can be entirely correlated with the Baal-Athtar myth.
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https://digitalcommons.liberty.edu/cgi/viewcontent.cgi?article=1279&context=lts_fac_pubs
See What is the correct translation of הֵילֵ֣ל?; ends with:
The third case of "Wail" seems to make the most sense from the context, and the hermeneutics is especially great, but can anyone verify with some reference or authoritative source that "the Hif'il imperative conjugation of the lemma יָלַל (yalal) is הֵילֵ֣ל?"
In the comments:
@andrewmh20 It's not a full explanation yet because it doesn't answer the question of how grammatically הֵילֵ֣ל descends from הָלַל; how is this case made? It's a similar question to how we might know יָלַל conjugates to הֵילֵ֣ל –
ahnnyoung
Sep 3 '15 at 18:32
@ahnnyoung I don't think that's really relevant....obviously they are related, but one does not directly descend from the other. The Lexicon brings the verb הלל, and it's conjugations...but הילל is amount, not a verb so there is no "descent", at least how I understand your question. The Lexicon cross references the Assyrian "mustilil" if that helps... –
andrewmh20
Sep 3 '15 at 18:53
See How many times does the Hebrew word הֵילֵל (heilel) occur in the Masoretic text?