Not familar with your particular Audi but you say the fuse #3 controls dash/instrument lights and headlight washer, right ? Does the headlight washer pump work ? Can you see if the wires at the back of the fuse box coresponding with position #3 shows signs of overheating/charred connectors ? The time when the fuse blows is not associated with hitting some switch, signal stalk, turning on highbeams, right? It blows with everything off except for the steady state dash lights...? Somewhere there is a short which is drawing too many amps which may be the headlight washer pump(doubtful since it would blow fuse only when activated), the headlight washer switch, or possibly the dashlight rheostat for adjusting the brightness level. Sounds like a bit of a job to check the involved wiring to see which one might show signs of overheating or charred connector. No evidence of water behind dash, fuse box area, wet soundproofing or carpet when stuffing your hand up behind ? Nothing easy like the wrong, lower rated fuse in #3, I guess.

Good luck,

Craig