Thanks for all those possibilities. The strange thing is that just touching the metal case to ground stops the horn from working, still get the click but no horns. I'll try to take the relay apart and see where things might be causing the problem. Else I guess I can either insulate the metal mounting part, leave it hanging or last resort, get a new one.
Troubleshooting things over the internet can be fun.
Are you sure it is the correct relay for the car ?.
I'm not up to full speed with your year and model, but does your horn relay also contain the key buzzer circuit ?.
Just to keep things straight and not to keep going over this but if you have the horn relay not mounted and just dangling in the air and then someone else pushes the horn button on the steering wheel and the horn blows, the second you touch the relay to the radiator support the horn quits sounding while this someone else is still in the car pushing down the horn button on the steering wheel and then if the relay is taken off of the radiator support the horn then again starts sounding ?.
If this is what happening, is there any electrical arc when the relay touches the radiator support and then the horn quits sounding ?.
I know I was curious as to what was inside my combination horn relay/key buzzer and it really wasn't bad taking it apart. The little peened over edges of the stamped tin can were pried open with a screw driver and then when I went to put it back together I was able to hold it and position a screwdriver to tap it with a hammer and peen the spots back over again.
If you can, take some high resolution pictures of the relay as is and then if it is taken apart, take some at that point also. I do kinda wonder if maybe something screwy is going on with the coil inside that pulls the contact points together.