The interpretation of the origin of vel from a second person indicative of volo is proved by the comparison with the Umbrian "heris - heris", 2. pers. from *herio = volo (Hofmann – Szantyr p. 501). You can compare even the modern Greek "θέλεις - θέλεις" or the Italian "vuoi - vuoi", which have the same meaning of the second person indicative of volo and in that case could be translated with "either - or" (Thumb, p. 173).
The origin from an old imperative of volo is formally and semantically impossible (Jacobsohn, p. 344), and it is more likely that the form "vel" derives from *vell < *vels due to proclisis (Jacobsohn, p. 348). For other hypothesis, see Walde – Hoffmann p. 743.
The semantic development started from an interrogative form
("do you want?" "if you want"):
Plaut. Aul. 452: etiam intro duce, si vis, vel gregem venalium
Cic. Planc. 79: agitur studium tuum vel
etiam, si vis, existimatio, laus aedilitatis
Cic. Tusc. 3,18: qui sit frugi igitur vel, si mavis, moderatus et temperans
Catull. 55,21: vel, si vis, licet obseres palatum
Then it became gradually widespread into the disjunctive form ("or if you want", "if you prefer"):
Plaut. Pseud. 31: lege vel tabellas redde
Plaut. Poen. 1382: utrum vis est, vel leno vel Lycus
His connection with volo is thus expressed by the possibility of choice between the two terms.
Bibliography:
J.B. Hofmann – A. Szantyr, Lateinische Syntax und Stilistik, München 1972.
H. Jacobsohn, Got. Ōgs, Lat. Vel, "KZ" 45, 1913, pp. 342-348.
A. Thumb, Handbuch der neugriechischen Volkssprache, Straßburg 1910.
A. Walde – J.B. Hoffmann, Lateinisches Etymologisches Wörterbuch, II, Heidelberg, 1954.
