A root for “nine” introduced in The Etymologies of the 1930s (Ety/NÉTER), replacing earliest words for “nine” such as ᴱQ. olme(t) and ᴱQ. hue from the 1910s and 20s. The root continued to appear in Tolkien’s later writings, and in his notes on Eldarin Hands, Fingers and Numerals from the late 1960s he explored several possible origins for this root: connected to the finger name Q. nettë “little girl” derived from the root √NET “dainty” (VT47/33), based on the counting term Q. nete “one more” as in “nete, nete, nete, 10” (VT47/15-16), or simply as an independent invention of its own (VT47/12).
Neo-Eldarin: For purposes of Neo-Eldarin, I think it is easiest to assume √NETER its own root without any deeper etymology.
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.