No melted connectors, but I did get this advice on another Mustang message board that seems to have done the trick:
"I permananetly fixed my 89 GT myself that did this. Take the contact pad out. Peel the two plates apart. Get some gray open cell packing foam from somewhere and cut some small slices out the same thickness that the old foam was before it collapsed...maybe just a bit thicker. Cut small squares and glue the squares all over (you'll see when you tear into it). Glue the plates back together."
http://forums.stangnet.com/showthrea...=1#post6733291
When I took the plates apart, there was almost no padding to be found, which would mean an almost constant connection being made and that is what caused the horn to go off and be stuck as well as the clicking noise after the horn was disconnected. Hope that info helps anyone else experiencing this same problem!