Sounds like a supply is going straight to earth.
Maybe just a bulb holder fault in which case you could try removing all the bulbs in the circuit which is blowing. If the fuse doesn't blow then, try replacing the bulbs one at a time.
Alternatively you could try a continuity test between the live side of the bulb holders and earth and see if you get a circuit, in which case that would mean a short on that feed.
What about the unit that operates the bulb failure lights, could that somehow cause this problem?