i had the same problem on my project car last time i drove it. haven't had time to look at it yet, so haven't solved it, so would also be interested in some answers please.
my first thought is to check te switch on the steering column, then the relay.
but there's no way it can be the bulbs if the hazards still work

and anyway, there's 3 blbs for each side so even more unlikely to all blow at once.