An element in the word gwahae, itself an element in Gwahaedir which was the Sindarin name of the palantír from drafts of The Lord of the Rings appendices (PM/186 note #15). In The Etymologies of the 1930s, the word N. gwahae was the equivalent of ᴹQ. (a)vahāya under the root ᴹ√KHAYA “far, distant, remote” (EtyAC/KHAYA), so likely meaning “*far away”. Therefore, the prefix gwa- probably means “away” and is based on the root √AWA.

Note, however, that in the Quendi and Eldar essay of 1959-60, Tolkien said:

Sindarin. The only normal derivative [of AWA] is the preposition o, the usual word for “from, of”. None of the forms of the element *awa [“away”] are found as a prefix in S, probably because they became like or the same as the products of *wō, *wo [S. go-, gwa- “together”] (WJ/366).

Neo-Sindarin: Despite Tolkien’s later statement that √AWA was not used a prefix in Sindarin, I think it is worth retaining gwa- “away”, as we have no better alternatives. Of the two variants of the prefix go-/gwa- “together”, go- is much more common and gwa- appears only in a few older forms like gwanon “twin”, usually of obscured meaning. I think that leaves enough semantic space for the prefix gwa- “away”. I would also use ᴺS. gwa “away” as an adverb in Neo-Sindarin. I rationalize these choices as being derived from inverted WA rather than AWA, and thus not technically in conflict with Tolkien’s notes in Quendi and Eldar; compare gwanwen “departed” < WA also appearing in that essay (WJ/378).