gay, proud, so Irish; from uaill.
pride, Irish uaill, Early Irish úaill, Old Irish uall: *oukslâ, root eu@g, ve@g of uasal.
This seems to be saying that uaill is from Proto-Celtic *oukslâ, the same source as uasal.
noble, proud, Irish, Old Irish uasal, Welsh uchel, Breton uhel, huel, Gaulish uxello-: *oukselo-, high, root eu@g, ve@g, rise, increase; Greek @Gu@`yclós, high, @Gau@'xw, increase; Latin augeo, increase, vigeo, be strong; English up, German auf; Lithuanian áuksztas, high.
MacBain's is conflating a bunch of Proto-Indo-European roots here; the relevant one, as reported by The Etymological Lexicon of Proto-Celtic and Pokorny is *upo- "under, up from under, over".
This derivation of hooligan is not in any published sources as far as I can tell. But maybe there's something to be investigated here.
The most interesting reflex of *upo- is Sanskrit उपल upala "stone, gem", which was borrowed into English as opal. Hobson-Jobson says "We do not know how the Skt. word received this specific meaning", but the AHD connects it to उपर upara "lower; later; nearer; m. the nether stone (on which Soma is pounded)" from उप upa "below".