Ghost-
Try turning the steering wheel to different positions and pushing the pad. Sometimes the slip ring on the cancelling cam gets dirty/worn so it doesn't get good contact with the brush sticking out of the turn signal switch. If the blaster worky with the wheel turned to a different spot, this might be your problem. You also might want to swap horn relays from another Jeep to see if that makes any difference.
Not much to testing the horn switch (pad), if yours is like the base wheel in mine, two screws in the back to remove the pad, two wires, jump across them to bypass the switch. I'm not familiar with the 3 spoke wheel Sleepydog has, but if it has no wire to the center cap (and no switch) like he describes, i'm guessing it's like other GM wheels, the center cap has plastic tabs that snap into a metal cup or ring that holds it in place. The cup/ring is 'hot', and by pushing the center cap you tilt the cup/ring and ground it to the wheel.