I have usually found these issues to be a lack of a good ground. The horn MUST have a good ground from the bracket to ground. Was the bracket removed and painted? If so, could the continuity from the bracket to inside the horn be coated with paint?
It sounds like you are testing all the right things. Just make darn sure the horn has a good ground as it would be too much if a coincidence for BOTH to quit at the same time. (And like
@340wedge noted, be sure to see if 12v is being applied at the horn spade when you hit the horn button.)