Once again, everyone - thanks for your help! My horn works as it should now...I'm posting my particular fix, just so's some other hapless future owner can consider it:
The entire horn button assembly (might only apply to my year, my builder) is a press fit. Insert something sturdy and extra-slim in the holes behind the hub, and sequentially whack on it. Eventually, the whole thing greets you by popping off. Be careful if you want to pry out the black plastic piece once you're holding the unit in your hand; it's brittle. That too, is press-fitted into the chrome ring.
Not trusting the grounding ability of the tab end at the end of the copper contact strip in side the assembly, I soldered a piece of 14 gauge wire to it, connecting the other end of the wire to one of the three lil bolts down in the hub.
The red wire traveling down the shaft and eventually exiting at the shaft's base jumps over the insulating donut and connects to a bolt head on the other side of the flange; I made sure the connection was nice and clean...and double-checked, during the process, that my entire steering shaft/column was NOT grounded, but in a neutral state.
THEN...I ran a new wire from one of the horn terminals back into the passenger compartment, going through the firewall...carefully drilled a small hole in the steering tube; I attached that ground wire there, using a small (and very short - this is important; there's a steering shaft running through that tube, you don't want to make contact) self-tapping screw. And, like they say, voila. Press on the horn button, the steering tube becomes grounded, the horn beeps.
Mebbe not particularly elegant. But hardly noticeable. And the maddeningly simple thing works. I still can't figure how the setup was wired in the first place - but the problem's history now.
So - once again, thanks for all the very helpful advice.
