In 38 years of owning my AA-1B, that is one thing I have not had to work on. The symptom of the horn staying on sounds like the circuit going out to the switch is grounding out, either by a bad switch (on the wing) or a wire between the horn behind the panel running to the switch is grounding out somewhere. I would pull the wire running out to the wing (switch) and see if the horn stops. Assuming it does, then it is matter of troubleshooting the wiring or the switch. If the horn still sounds, it might be the controller.
Serviceable controllers and switches are hard to find, but if you think you have a bad one, check with the usual suspects like Roscoe at Yankee Aviation and Fletchair.