John,
There are normally 2 places for the gear horn to operate. One is the throttle switch and the other are the gear safety switch out on the main gear. (Sometimes on one gear sometimes on both). I am not sure how you got the horn to work by tapping the switches on the motor unless you actuated it and it was telling the gear warning that the gear was not safe. I am assuming you are doing these checks on jacks. With plane on jacks and gear in up position pull the throttle to idle. If the horn does not operate you have a problem in the micro switch throttle circuit.
With gear in down position, disconnect both or the single gear safety Switches. If you have a single gear safety switch, after disconnecting the rod, select gear handle to up position and turn Master Switch on. Horn should operate telling you the gear handle is in the up position on the ground and gear should not move. If horn does not sound or gear starts to retract, Safety switch is bad.
On dual safety switch system disconnect both switches. Pull down on one switch to the extended position and turn the master on horn should operate and gear not move. TURN MASTER OFF!!! Release that safety switch and pull down on the other safety and turn MASTER back on. Gear should not move and horn sound. TURN MASTER OFF and reconnect both rods. MAKE SURE YOU TURN MASTER OFF BETWEEN CHECKING LH AND RH SWITCHES!!!!!
These are the only test I know for your gear horn and should isolate your problem.