The wire just needs to be grounded to activate the horn. When you press the horn pad it closes the ground circuit to activate the horn.
You may be missing the turn signal canceling cam, it mounts behind the steering wheel and has a plastic cylinder that extends through the hole at 10 0'clock. From there a bayonet fitting and spring hold a wire that connects to the back of your horn pad.
If you see a wire in the hole, it may be the wire that connects to the contact for the TSCC OR A BROKEN WIRE HELD IN BY THE ORIGINAL bayonet mount. The wire I show is made by Dorman and is universal, you may have to trim the barrel at the opposite end of the bayonet mount to use the one I show.
The turn signal canceling cam is made for tilt and non tilt wheels, so you have to get the one for your application. Doesn't look like you have tilt.
I'll see if I can find some part numbers or suppliers for you.
If you can't see the bayonet mount in the hole of the steering wheel, you'll have to pull the steering wheel. If you do that, post a picture so we can see what's going on in there.