The usual word for “star” in Sindarin which replaced archaic/poetic êl; it originally meant “(bright) spark” (RGEO/65; VT42/11). It was derived from the root √(Ñ)GIL meaning “shine (white)” (PE17/152) or “silver glint” (MR/388; PE17/22).
Conceptual Development: This word first appeared as G. gail “a star” in the Gnomish Lexicon of the 1910s (GL/42), derived from the early root ᴱ√Gil- (GL/38). In the Early Noldorin Grammar Tolkien said ᴱN. gail meant “sign, token, heavenly body” (PE13/123); earlier in this document he gave it the gloss {“life” >>} “sign” (PE13/120 and note #6). In Early Noldorin Word-lists written somewhat later, gail again simply meant “star” (PE13/143), and it was used this way in the Nebrachar poem from around 1930 (MC/217).
In The Etymologies of the 1930s Tolkien gave it as N. geil “star” from primitive ᴹ✶gilya under the root ᴹ√GIL “shine (white or pale)” (Ety/GIL; EtyAC/GIL). Christopher Tolkien incorrectly marked geil as a plural form in The Etymologies as published in The Lost Road (LR/358), but Carl Hostetter and Patrick Wynne corrected this in their Addenda and Corrigenda to the Etymologies (VT45/15). Remnants of this 1930s derivation can be seen in the forms geil/gail in notes from the 1950s, derived from ancient ✶gilyā “silver spark” (PE17/30, 152). Mostly, however, Tolkien represented this word as gil in later writings, including in The Lord of the Rings Appendix E (LotR/1113).
Possible Etymology: The etymology of gil is complicated by Tolkien’s vacillation with the singular form gail (†geil) < ✶gilyā, where the diphthong ai is the result of a-affection of the base vowel from i to e, which after i-intrusion produced ei and this diphthong became ai as usual in final syllables and monosyllables: gilyā [ >✱geli(a)] > geil > gail. Signs of this etymology can be seen in the class plural giliath as in S. Dagor-nuin-Giliath “Battle-under-Stars” (S/106).
With this alternate derivation, the plural form would still be gîl, since the ancient plural -ī prevented a-affection, and the prefixal form likewise would have been gil- (PE17/152). However, this derivation conflicts with Tolkien’s usual presentation of the singular form as gil. In some places Tolkien gave a primitive form like ✶(ñ)gillē (PE17/23) or a Sindarin form gill (PE17/50), but I think it is best to assume primitive ✱gili- to explain singular gil and class-plural giliath.
In The Etymologies (Ety/358, corrected by VT/45:15), this word was given as geil , plural gîl. However, later in LotR/E and RGEO/73, Tolkien seems to consider gil as a singular (with no hints in the sources of what the plural would be, besides the collective plural giliath )