Most standard HORN buttons are a spring loaded push pad..that activates a GROUNDED Contact (looks like a motor brush..carbon contact with a spring between the contact ends) that contact goes through the steering wheel inside of a plastic insulator, the other end sticking out of the bottom of the steering wheel..all of this part moves with the wheel..
The Column side has a "Copper Ring" that goes around the steering wheel shaft..(this part does not move ) and hooks to the black 20 ga wire in the column..the contact touches this when the button is pushed..and fires the relay coil by providing GROUND to the relay..sounding the horn..
This is why I was concerned when you said you applied 12 volts to the horn button wire..If you follow it out..you have 12 volts at the bottom of the column..then when you sound the horn button...you ground that 12 volts directly through the horn ring...ERGO...Smoke...Fire and wires going away inside the column..Dead Short..
You Should Not be able to run power through a standard GM horn button, as it mechanically grounds inside the column..
This is also why the relay is wired Power for the relay coil directly to 12 volts hot at all times...and relay coil ground to the horn button..
I hope you follow what I am saying..It's like taking a button and putting + from the battery on one side of the button, and - from the battery on the other..It's fine til you push the button..then you let out the factory installed smoke..