This root first appeared as unglossed ᴹ√MEN in The Etymologies of the 1930s, where it seemed to be stationary in nature given its derivatives ᴹQ. men “place, spot” and ᴹQ. ména “region” (Ety/MEN). It was an element in direction words like ᴹQ. formen/N. forven, apparently meaning “✱north place” at this conceptual stage. In Demonstrative, Relative, and Correlative Stems (DRC) from the late 1940s, Tolkien first glossed ᴹ√MEN as “place, spot”, but that instance of the root was revised to ᴹ√NOM (PE23/112 and note #12), and a bit later in the same document Tolkien gave a new meaning to ᴹ√MEN as “purpose, aim” (PE23/112).
In the Quenya Verbal System (QVS) from 1948, Tolkien first gave ᴹ√MEN the gloss “aim at, intend, purpose” with the more specific sense “make for, proceed towards” when used with the allative, but then crossed this out and simply made the gloss “go, proceed” (PE22/103 and note #21). In Common Eldarin: Noun Structure of the early 1950s, Tolkien first gave √MEN the gloss as “place, situation, site”, then revised it to “direction, object, point moved toward” (PE21/79 and note #39).
Thereafter Tolkien mostly gave this root the basic sense “go” (PE17/93, 143, 165; VT39/11; VT42/32). Tolkien gave a somewhat lengthy description of the root in Definitive Linguistic Notes (DLN) from 1959:
> √MEN go, move, proceed in any direction (irrespective of speaker’s position, or assumed point of thought). mēn- a way, a going, a mov[ement] (PE17/165).
Thus in the 1950s and 1960s, Q. formen likely meant “✱north way” rather than “✱north place”. However, in a footnote in The Road Goes Ever On from 1967, Tolkien did say that men had the meaning “direction, region” as part of an explanation of √MENEL “heavens” = men + el (“region of stars”), so it seems Tolkien did not entirely abandon the use of this element as a name for places.
Neo-Eldarin: For purposes of Neo-Quenya, I sometimes see √MEN use for movement in general (as in motion picture) rather than movement in a direction. I personally recommend using ᴱQ. lev- “(intr.) move” from Qenya Wordlists of the 1920s for that purpose (PE16/132) since I think it is important to distinguish “move” from “go”, but if you prefer to use only later words you might be more comfortable expanding the semantic scope of √MEN to movement in general.
@@@ 1950s mendë “will” = “✱intent” and 1964 menta- “have as object, (in)tend”
A root meaning “go, proceed” appearing as one of the many etymologies of Q. vanwa “gone, departed”. It may have been a partial restoration of the (rejected) meaning of the root ᴹ√AB “go away, depart” from The Etymologies of the 1930s, a root that later was altered in that document to mean “refuse, deny, say no” (Ety/AB). It may also have been intended as a replacement for ᴹ√WAN “depart, go away, disappear, vanish”, also from The Etymologies and the basis for ᴹQ. vanwa in the 1930s.
In the published corpus, the first clear mention of this root is in a discussion of the Quenya future suffix -(u)va from the late 1940s where it was given as √BĀ, BANA “go, proceed” with Q. vanwa “gone, over” as one of its derivatives (PE22/97). It appeared again in a discussion of the Sindarin greeting mae govannen “well met” from the late 1950s, where Tolkien hypothesized that the verb “meet” might be go- “together” + ban- “go” or “meet”, which he again connected to Q. vanwa “gone” (PE17/16). Phonetic complications prompted Tolkien to coin a new verb covad- “assemble, gather together” from a root √KOB, but he was unwilling to commit at this time to the new verb because of the obvious similarity of govannen to √BAN “go” (PE17/16-17).
However, in 1959 when he was overhauling the Eldarin system of negation, it seems Tolkien finally rejected √BA(N) “go” because of the conflict with √BĀ/ABA “refuse”, and he transferred the sense “go” to the root √MEN (PE17/143). In etymological notes contemporaneous with the Quendi and Eldar essay of 1959-60, Tolkien restored √KOB “gather” (PE17/150) though he seems to have eventually settled on the form √KOM for this root along with a restored verb S. covad- “bring together, make meet” (PE17/157-158). Q. vanwa “gone” was also transferred to √WĀ/AWA by the time of the Quendi and Eldar essay (WJ/366). Meanwhile, the Quenya future had been transferred from √BA to the root √UB in the early 1950s (PE22/132).
This left no remaining functions for √BA(N) “go”, and there is no further sign of it starting in the 1960s.