An impersonal verb appearing as N. eil “it is raining” in The Etymologies of the 1930s derived from primitive ᴹ✶ulyā- (> œil > eil) under the root ᴹ√ULU “pour, flow” (Ety/ULU; EtyAC/ULU). This verb is abnormal in that its final a disappeared rather than surviving as it usually did for derived verbs, giving eil rather than ✱elia-, ✱eilia- or ✱eila-. However, as an impersonal verb there would never be any pronominal suffix to help preserve the final a by analogy, which probably explains the vowel loss.
Conceptual Development: The verb for “rain” in the Gnomish Lexicon of the 1910s was G. ubra-, probably related to G. ub “wet, moist, damp” (GL/74).
Neo-Sindarin: In Sindarin, the likely developments of primitive ✶ulyā would be to ✱oly(a) > ᴺS. uil “it rains”; I believe this form was first suggested by Helge Fauskanger in his Parviphith Edhellen wordlist. Compare ᴺS. uil to: S. ruin “fiery red” < (perhaps) ✱runyā and S. fuir “north” < (perhaps) ✱phoryā, and see the entry on how [[s|[œi] became [ui] or [y]]] for further discussion. Any inflected forms would probably restore the stem, such as (hypothetical) intransitive past and future forms ✱eilias “it rained” and ✱eiliatha “it will rain”).
An impersonal verb for “rain” attested only in its future form uluva “it is going to rain, it will rain” (PE22/167). Its aorist form is probably ✱ule “[it] rains”, its past form probably ✱úle “[it] rained”, and its perfect ✱úlie “[it] has rained”; as an impersonal verb, no explicit subject is required in Quenya. It is clearly derived from the root √UL “pour (out), flow” (WJ/400; PE17/168) and it seems that its primitive form originally meant “pour” (PE22/133), but elsewhere Tolkien gave the Quenya verb for “pour, flow” as ulya- (Ety/ULU).
Conceptual Development: In the Qenya Lexicon of the 1910s, the verb for “it rains” was (3rd-singular) ᴱQ. uqin from the early root ᴱ√UQU “wet” (QL/98). This verb reappeared as uqe or úqe “it rains” in the Early Qenya Grammar of the 1920s, having become an impersonal verb (PE14/56, 85). Another impersonal verb for “to rain” appeared in Quenya Verbal System of the 1940s: ᴹQ. kelya “(it) sends running down = it rains” from the root √KEL (PE22/114). The form uluva mentioned above appeared in Late Notes on Verbs from 1969 (PE22/167).
Neo-Eldarin: Based on attested forms I would limit ul- for “rain” as an impersonal verb only, and for “pour” would use ulya-. Interestingly, the Noldorin word for “rain” is eil [ᴺS. uil] from ᴹ✶ulyā-, so I think Quenya and Sindarin/Noldorin made different choices for which ancient verb became impersonal “rain”.