Why is it that when I start Miss Tilly, the Ahooga Horn will not sound right until I rev the engine a couple of times? After starting, the ammeter shows negative until revving the engine, then it pops right up to center and the horn sounds great.
The voltage level of your battery is lower that that of the generator or alternator you are running. When it kicks in the voltage level available to the horn is higher. You might try turning the adjuster on the horn down a click or too see if it will work just from the battery.
You could also try cleaning the battery ground strap where it attaches to the frame. Also clean the area of the frame where the strap bolts to.