Must be a slow fuse. The electrical schematic shows the horn on a 7.5 amp circuit with the brake and turn lights. My Fiamm horns ran 3.8 amps for the low one and 4.2 amps for the high one when I tested them. Two turn signals and the brake light should be 6.3 amps on top of that.
CORRECTION (30 Sep 2012): I misread the electrical diagram. I confused pink/blue with red/blue. The only thing on the circuit with the horn is the brake and tail light - not the turn signals.