I like the horn!

I know nothing about that design. Just by looking at the picture, I think the two batteries are in series, in which case, there is a remote chance each battery might be six volt each and two in series will give out 12v. If on of those two are bad, than it will not charge.

The toggle switch looks as if one blade connector is not hook up in the picture. That would be the terminal on the right in that picture. If that is the case. The switch only makes if it is in the right position and what ever those wires on each of those terminal will make. Trace out those wires from the switch and see where they go. Maybe they go to the horn but who knows unless you trace them out.

Is that small square box behind the switch part of the setup? I'm thinking maybe a rectifier?