Stock horn had battery power to one terminal...
Thanks Bill. I had already confirmed power. The truck is re-wired to 12v with a negative ground. This is the American Auto-wire harness - it's pretty awesome. I was able to trace the whole thing out and I have power to the horn (via a relay inside the cab). I can ground the horn wire which closes the relay, providing 12v to the horn. The horn does make a relay click sound - but that's it.
I attempted to clean the contacts, but this didn't seem to do much. I suspect the contacts are shot.
I am trying to make sure I understand the mechanism... Since sound is produced by vibration, the horn must be creating a pulsation or vibration. I'm guessing the contacts inside are meant to energize the coil, pulling the bar which moves the metal diaphragm and opens the contact (disconnecting the coil). Once the contact is broken the contacts close again the coil re-energizes... Is this about right? If this is correct, then my contacts are fine - otherwise the coil couldn't energize and make that relay sound. It also implies that the distance of the gap is very important - it would effectively set the frequency of the horn.
I ask about the inner workings because this would help me diagnose.