I'll bet it's the brass ring under the steering wheel.  Does it make a nasty
grinding sound, or any sound, when you turn the wheel?

This thin brass ring wears even thinner, then tears apart, then the pieces
ground themselves in the steering column.  The thing to do is pull off your
steering wheel and have a look.  Unclip the big pad in the middle, take off the
big nut holding the wheel on, then pull straight out.  ***Mark the steering
wheel and spindle so you put it back on correctly!!***  Look under the bottom of
the steering wheel -- if the brass ring is intact, check for a ground in the
switch itself, then check for worn wires under the steering column.

If it helps to visualize, the horn itself has constant +12V power, and the
horn button grounds from the steering column to connect the negative end of the
circuit.