How to test the horn
Horns draw a fair amount of current. You need a large wire, say n0 14, and not a "Radio Shack clip lead" LOL to test them.
Usually if they are bad, they will sort of "click". There's an adjustment screw which in reality is adjusting the electrical contact. These often get corroded, and sometimes you can "work" the adjustment back and forth a 1/2 turn or so and get it to start working again.