My bet is the clockspring connector inside the steering wheel is the culprit. The clockspring is a coiled electrical connector, it's not really a spring, inside the steering wheel that connects the horn button and air bag to the rest of the Jeep. Before jumping on that though, at least try swapping the horn relay for a different relay inside the Power Distribution Center. There are several relays inside there you can swap with the horn relay to make sure it's not just a bad relay.
I had an issue like this a couple months ago. Pulled horn switch and checked distribution box on passenger side under the hood. Underneath the box where all the wires are the wire for the horn was frayed I'm assuming from bouncing around and rubbing on something metal. I took some tape and covered wire back up and it hasn't had the problem since
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