Could be a short in the switch or clock spring in the steering wheel, a short in the wiring or a bad horn relay. I'd start with the least expensive item--the horn relay. That's also the most likely culprit--although I have heard of clocksprings and switches going bad.

 

I had this problem in a Town Car. The horn switch was shorted. That's what happened to you. After the horn blow long enough the fuse probably blew. That's why by the time you got there the horn stopped. It could have been the relay, but that's unlikely. The relay would have to be told falsely to energize. It could happen, but I doubt it. Besides you could check the horn relay with a DVOM to see if it's good or bad. It's not the clock spring because it is a N.C. contact. If it failed it would fail OPEN and the horn would never blow if the clock spring failed instead of blowing all the time which is what happened to you. The customer told me the dealership wanted $800.00 to fix this problem. That's because the horn switch is inside the Air Bag. You can't fix a shorted horn switch. You have to replace the whole Air Bag assembly for $800.00. What I did was removed the Air Bag and drilled a small hole thru the steering column at the top as far back as I could in the space where the Air Bag was removed. I then cut the harness going to the horn switch(it was shorted so it was defective anyway). I soldered some speaker wire to the harness where I cut the harness and shoved it thru the hole I just drilled. I put the Air Bag back in after reconnecting it. I then installed a Doorbell switch where the wires come out of the top of the steering column. It works and it only cost $5. The customer says it is OK because she only blows the horn once a year when she takes it in to have it inspected.