it does sound like a relay problem, but it could also be a problem with the combination switch ? i had one before which switched off all the lights when i indicated right, and flashed the high beams when i turned left !!
i know you said it was new, but it wouldn't be the first time i've bought a defective new part ?
take the steering column shroud off, and put a tester on the wires which go to the top of the combination switch. (with it switched off)
there's one (i think it might be red? not 100% sure tho?) which is live permanently. if you find any more than that, it's most likely to be the switch itself.
if not, either a broken/chafed wire, or a faulty relay are the most likely causes.
you also have to factor in that it's an alfa, they seem to do things just because they can ! most annoyingly, by the time you get close to finding it, it's fixed itself, so you never know what the problem was in the first place !!
you're never alone with schizophrenia.
1992 alfa 75 2.0 twinspark l.e. (one of the last) now sadly departed
1971 mercury cougar. 302c.i., lightly tuned
1995 volvo 850 t-5 240 bhp the new toy !