try jumping the horn itself like stated, also (dumb question) where you hitting the horn button in the car when you checked for voltage at the plug? was the car on?

check for power to the relay, one should be constant, one should be switched with the horn on the steering as a switch. if you have both of those then check for power leaving. this will be switched too.

if the horn beeps when jumped to power, and the relay has power to it, then my guess is nothing is coming out.
which would mean you need a relay. but the is possibility of it being something else.