A root appearing in a pair of notes from around 1969 glossed “net; knit (contrive a network); catch, involve (in a net)” (PE22/159) and “net, knit, contrive network or lace; {catch,} involve in a network, enlace” (VT42/12), in both notes serving as an explanation for the name S. Gilraen. Both notes have a similar set of derivatives such as Q. raima/S. raef “net” and Q. raina/S. raen “netted, enlaced”. In the second note this root was compared to √WIG and √REB/REM, the former used of weaving in general as opposed to √RAY used of lace-work with a single thread, and the latter a verbal root having to with netting via traps and snares such as by hunters and fisherman. This comparison to √REB/REM was probably related to the deletion of the gloss “catch” from the second note.
These notes probably replaced another etymology of the name S. Gilraen in notes from the late 1950s where √RAY was glossed “smile” and “show pleasure or favour in facial expression” with derivatives like Q. raina/S. raen “smiling” and contrasted with the root √LALA “laugh” (PE17/182; VT44/35). This in turn might have been connected to Q. rainë “✱peace, good will” in Quenya prayers from the 1950s (VT44/34).
Neo-Eldarin: It is very unlikely Tolkien ever considered both √RAY “knit” and √RAY “smile” to be part of Elvish at the same time. Unfortunately, the latter is the most popular source of “smile” words in Neo-Eldarin; the only other option is the very early root ᴱ√MIRI or ᴱ√MṚT͡YṚ “smile”, whose derivatives clashes with the later and very well-known root √MIR “precious” used for jewels. It is therefore difficult to eliminate √RAY “smile” in favor of √RAY “knit”, itself with a large number of useful derivatives. For now, I recommend keeping both as part of Neo-Eldarin, even though they were probably incompatible in Tolkien’s mind.
A root element Tolkien gave unglossed in notes on Eldarin Hands, Fingers and Numerals from the late 1960s serving primarily as the basis for extended √NETER “nine”; Tolkien explicitly contrasted it with √NETH “sister”, used for the finger-name of the fourth and ninth fingers but not etymologically related “nine” (VT47/11-12). However in somewhat earlier versions of these notes from 1968, Tolkien glossed √NET as “trim (pretty, dainty)” and derived the finger name Q. nettë “little girl” directly from this root along with other words like Q. netil “trinket” and netya- “trim, adorn” (VT47/33).
Neo-Eldarin: For purposes of Neo-Eldarin, I think it is worth retaining the “pretty, dainty” sense of this root, though not necessarily connecting it to “nine”, which can simply be from unrelated √NETER.