√TIL “point, horn”
The root √TIL was used for “pointy thing” for much of Tolkien’s life, most notably as the final element in the name Q. Taniquetil “High White (or Snow) Peak”. Its earliest appearance was as unglossed ᴱ√TILI⁽²⁾ or ᴱ√T͡YILI (probably the true form) in the Qenya Lexicon of the 1910s, where it had derivatives like ᴱQ. til⁽²⁾ “a hair”, ᴱQ. tilde “point”, and ᴱQ. tille “eyelash” (QL/92). It was constrasted ᴱ√TILI⁽¹⁾ which had derivatives like ᴱQ. tilu- “shine (blue)” and ᴱQ. Tilio “Sirius” (QL/92). There is no connection between √TIL and “shine” in Tolkien’s later writings, with roots like √SIL or √TIN being used for that purpose instead.
The Etymologies of the 1930s had ᴹ√TIL “point, horn” with derivatives like ᴹQ. tilde/N. till “spike, horn” and ᴹQ. neltil/N. nelthil (Ety/TIL). The root √TIL “point” was mentioned a couple times in notes from the late 1960s in connection to finger-names (VT47/26, 28).
√TIN “sparkle, spark, [ᴱ√] twinkle, [ᴹ√] emit slender (silver pale) beams”
The root √TIN was connected to Elvish words for twinkle and sparkle for much of Tolkien’s life. The root first appeared as ᴱ√TINI “twinkle” in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. tintya- “sparkle” and ᴱQ. tinwe “star” (QL/92). The root also had derivatives in the contemporaneous Gnomish Lexicon such as G. tim “spark, gleam, (star)” and G. tintiltha- “twinkle” (GL/72). In The Etymologies of the 1930s he had the root ᴹ√TIN “sparkle, emit slender (silver pale) beams” with derivatives like ᴹQ. tin-/N. tinna- “glint” and ᴹQ. tinwe/N. tinw “spark, (small) star” (Ety/TIN). The root √TIN was mentioned regularly in his later writings with glosses like “spark” or “sparkle” (MR/388; PE17/22, 66).
ᴹ√TING “ting (onomatopoeic)”
An onomatopoeic root with variants ᴹ√TING and ᴹ√TANG appearing in The Etymologies of the 1930s with derivatives ᴹQ. tinge or tango “twang”, ᴹQ. tinga- “to twang”, and N. tang “bowstring” (Ety/TING). The entry had a reference to a deleted variant ᴹ√THING (EtyAC/TING) and another variant ᴹ√TUNG was listed in the entry ᴹ√DING (EtyAC/DING). In the Quenya Verbal System of the 1940s Tolkien gave the root ᴹ√TAÑ as the basis for the verb ᴹQ. tanga- “twang”, which is probably another instance of this root (PE22/103).
The “root” ᴹ√TINKŌ (more likely just a primitive word) appeared in The Etymologies of the 1930s with the gloss “metal” and derivatives like ᴹQ. tinko/N. tinc of the same meaning (Ety/TINKŌ). The reappearance of Q. tinco “metal” in The Lord of the Rings appendices (LotR/1122) strongly indicates its ongoing validity.
ᴹ√TINKŌ may have replaced the root ᴱ√SINI “pale blue” from the Qenya Lexicon of the 1910s with derivatives like ᴱQ. sink “mineral, gem, metal” and G. sinc “metal” (QL/83; GL/67); these early mineral words were originally attributed to ᴱ√SṆT͡YṆ “twinkle” before they were transferred to ᴱ√SINI, leaving only derivatives like ᴱQ. sintl “crystal” and ᴱQ. sinty- “sparkle” under ᴱ√SṆT͡YṆ (QL/85). However, in notes from the late 1960s Tolkien had primitive ✶sinki as an element ✶sinkitamo, the basis for Q. sintamo “smith” (PE17/108). Likewise there is evidence of the earlier root in Q. sinca “flint” as in Q. sincahonda “flint-hearted” (LotR/979), initially given as ᴹQ. tingahondo in Lord of the Rings drafts (SD/68).
Neo-Eldarin: For purposes of Neo-Eldarin, I would definitely use ✶tink- = “metal”, but I think it is worth keeping ✶sinki = “*mineral” as a variant.
√TIR “watch (over), look at, observe, gaze at; [ᴹ√] guard”
Tolkien used the root √TIR for Elvish words for watching and looking throughout his life. The earliest manifestation of this root was in the Qenya Lexicon of the 1910s as ᴱ√TIRI “guard” (the gloss appeared under the entry for ᴱ√TIŘI) with derivatives like ᴱQ. tiri- “watch; keep, guard, preserve; look at, gaze at, observe” and ᴱQ. tirne “steadfast regard, stare” (QL/93). It also had derivatives in the contemporaneous Gnomish Lexicon such as G. tir- “look for, look out for, watch for, await, expect” and G. tirin “watch-tower, turret, tower” (GL/71). The Etymologies of the 1930s has ᴹ√TIR “watch, guard” with derivatives like ᴹQ. tir-/N. tir- “watch”, ᴹQ. tirion “watch-tower, tower” and N. tirith “watch, guard” (Ety/TIR). The root √TIR was mentioned regularly in Tolkien’s later writings with glosses like “watch, observe” (PE17/187), “to look at (towards), watch, watch over” (RGEO/65) or “look at (turn eyes to, keep eyes on, watch)” (PE22/155).
ᴹ√TIW “fat, thick”
The root ᴹ√TIW “fat, thick” appeared in The Etymologies of the 1930s with derivatives like ᴹQ. tiuka/N. tûg “thick, fat” and ᴹQ. tiuko “thigh” (Ety/TIW). Tolkien said it may have been the basis for the root ᴹ√TUY “spring, sprout” via the sense “grow fat, swell” (Ety/TUY), perhaps as an abnormal vocalization: *tiwy- > *t(i)u̯y-. Tolkien had a similar pair of related roots in the Qenya Lexicon of the 1910s: ᴱ√TIW̯I “thick” and unglossed ᴱ√TYU which was the basis for words like ᴱQ. tyû “thigh” (GL/50, 93); that document also had ᴱ√TUẎU as the basis for “sprout” and “spring” words, but in the 1910s it seems to be unrelated. Also in the 1910s, Tolkien had unglossed ᴱ√PIẆI with derivatives like ᴱQ. pingwa “fat, rich (of soil)” and ᴱQ. piu “calf of leg” (QL/74), which might have been another precursor to ᴹ√TIW “fat, thick” from the 1930s.
In the Outline of Phonetic Development (OP1) also of the 1930s, Tolkien instead gave ᴹ√KIWIK as the basis for ᴹQ. ciuca “thigh” (PE19/54). A similar etymology for Q. kiuka or kyūka “thigh” appeared in Outline of Phonology (OP2) of the early 1950s (PE19/107). Thus there was considerable variation in form for these roots.
Neo-Eldarin: For purposes of Neo-Eldarin, I’d stick with ᴹ√TIW “fat, thick” as the base root, as it has the large collection of derivatives.