This root and ones like it were used for “high” things for much of Tolkien’s life. It first appeared as unglossed ᴱ√TAHA in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. tā “high; high above, high up”, ᴱQ. tahōra or tayóra “lofty”, and ᴱQ. tāri “queen”; it had a variant form ᴱ√TAʕA where the ʕ might be a malformed Y (QL/87). The corresponding forms in the contemporaneous Gnomish Lexicon were G. dâ “high” and G. dara “lofty” (GL/29), indicating the true form of the root was ᴱ√DAHA, since initial voiced stops were unvoiced (d- > t-) in Early Qenya (PE12/17). Primitive forms like ᴱ✶dagá > ᴱN. dâ/ᴱQ. tá “high” in Early Noldorin Word-lists of the 1920s indicates the root continued to begin with D for the following decade (PE13/141, 161).
In The Etymologies of the 1930s Tolkien gave this root as ᴹ√TĀ/TAƷ “high, lofty; noble” with derivatives like ᴹQ. tára “lofty, high”, ᴹQ. tári “queen” and N. taen “height, summit of high mountain” (Ety/TĀ). In Definitive Linguistic Notes (DLN) from 1959 Tolkien gave the root as √TAG or Tā- “high”, and in notes from around 1967 Tolkien gave √TAƷ as the explanation of the initial element of Q. Taniquetil and contrasted it with √TĂR “stand” (PE17/186). In 1970 green-ink revisions to the Outline of Phonology (OP2), Tolkien wrote a marginal note giving √TAƷ > TĀ “high”, but this note was rejected with a statement “transfer to Gen. Structure. No [ʒ] existed in Eldarin” (PE19/72-73 note #22).
This last rejection seems to be part of Tolkien’s general vacillation on the nature and phonetic evolution of velar spirants in Primitive Elvish in 1968-70. For purposes of Neo-Eldarin, I would assume the root form was √TAH or √TAƷ > √TĀ as the basis for “high” words, much like √MAH or √MAƷ > ✶mā was the basis for “hand” words.
This invertible root had a long history in Tolkien’s writings. Its earliest iteration was in a pair of roots in the Qenya Lexicon of the 1910s: ᴱ√OŘO [OÐO] with derivatives having to do with the “dawn”, and ᴱ√ORO “steepness, rising” with which it was much confused (QL/70). The latter had derivatives like ᴱQ. orme “summit, crest, hilltop” and ᴱQ. orto- “raise” (QL/70), and Tolkien mentioned an inverted variant ᴱ√RŌ or ᴱ√ROHO with derivatives like ᴱQ. róna- “arise, rise, ascend” (QL/80). The contemporaneous Gnomish Lexicon also gave it as in an invertible root ᴱ√rō-, oro with derivatives like G. oros “rising” and G. ront “high, steep” (GL/63, 66).
The root reappeared in The Etymologies of the 1930s as ᴹ√ORO “up, rise, high” and ᴹ√RŌ “rise” (Ety/ORO, RŌ). The root was mentioned very frequently in his writings from the 1930s, 40s, 50s and 60s, generally glossed “rise” or “up(wards)”. Thus the root was very well established in Tolkien’s mind.