A root introduced by Tolkien in Definitive Linguistic Notes (DLN) from 1959 with the gloss “close eyes, blink, wink” to provide a new explanation for the flower name S. alfirin (originally “immortal = not mortal”) after he decided the prefix al- meant “well” rather than “not” (PE17/146). He derived the names Q. pirindë and S. pirin for “a flower that opened and shut quickly with any change of light”. The root ᴱ√PIRI also appeared (unglossed) in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. piri- “spin, turn”, ᴱQ. pirin “thin rod, pin” and ᴱQ. piruke “swirl, twisting, pirouetting” (QL/74). Finally, the word Q. pirë “toe” appeared in notes associated with the 1955 version of the poem Q. Nieninquë, perhaps representing a third meaning for this root (PE16/96).
Neo-Eldarin: For purposes of Neo-Eldarin, I think the gloss “blink, wink” for √PIR is not a great fit, since it is a contrived etymology Tolkien invented for a word he clearly meant to be something different originally. Q. tihta- is probably a better known verb for “blink”. For “spin”, I prefer a Neo-Eldarin root ᴺ√KWIR adapted from early ᴱ√QIŘI. However, I think ᴺ√PIR might be retained as a Neo-Root with the sense “✱cylinder”; I think this works as an explanation of Q. pirë “toe”, and allows the retention of early words like ᴱQ. pirin “thin rod, pin” and ᴱQ. pirinumbe “cylinder”.
Tolkien used a similar set of Elvish roots for “youth” and “freshness” for many years. The earliest of these was primitive guı̯u̯ or gu̯iu̯ [ᴱ√GWIWI] in the Gnomish Lexicon of the 1910s with derivatives like G. gui “just, just now, only just, already”, G. guin “recent, fresh”, and G. gwioth “youth” (GL/42). This root reappeared as ᴹ√WIR “new, fresh, young” in The Etymologies of the 1930s with variants ᴹ√WĪ and ᴹ√WIN and derivatives ᴹQ. vírie “youth” and ᴹQ. virya “fresh” (EtyAC/WIR). The ᴹ√WIN variant had derivatives ᴹQ. vinya/N. gwîn “young”. Tolkien considered, but rejected, deriving these from strengthened ᴹ√GWIN instead, producing (also rejected) ᴹQ. winya/N. bîn (EtyAC/GWIN).
Q. vinya appeared in quite a few later names with the gloss “young” or “new”, but the Sindarin form became S. gwain as in S. Narwain “January, ✱(lit.) New Fire” (LotR/1110) and S. Iarwain “Old-young” (LotR/1114; RC/128). In Definitive Linguistic Notes (DLN) from 1959, both were given as derivatives of √WIN “young” along with Q. víne/S. gwîn “youth”, though the Sindarin word for “young” was given as (archaic?) gwein (PE17/191). Also related are various words for “baby” from 1968 notes such Q. †wine/S. gwinig “little-one, baby” (VT48/6). In these notes primitive wini was glossed “little” but this was deleted (VT47/26), making it likely that the earlier senses “young, new” were restored for √WIN.
As for the 1930s root ᴹ√WIR, it might have survived as an element in the month names Q. Víressë/S. Gwirith “April” (LotR/1110), perhaps meaning “✱freshness”.