If you put a DMM on each side of one of the horn buttons (set to measure resistance (the 200 ohm scale is fine), with the button at rest your meter should read open circuit (often depicted with an I on your screen). Push the horn button and the reading should drop to a reasonable reading (less than 100 ohms, though I'd have to look up the actual spec. It would not matter because we'd move to testing the same signal at the relay next anyhow).
If this continuity doesnt occur, the relay doesnt 'know' that you're hitting the horn button.
The only reason I brought that up is that I've seen the horn button pads wear and the horn would not activate. In other words, the meter would always read I, even if the button was mashed through the steering wheel.
Just be very careful when working on this, as you're close to the airbag wiring.
And I still think it's a clockspring issue.