Here is how your horns are supposed to be. The first diagram is the 64 1/2 horns, which have a horn relay and only one wire for a contact in the turn signal switch. I'll talk about those in a later post. Right now you can only see part of the wiring diagrams, but, if you click on one of them, the rest of it will show up. The rest of this is post is for the 65/66 cars that have an alternator instead of a generator.
The first picture is the wiring of everything horn-related that isn't right behind the steering wheel. The last picture is a new turn signal switch. This one is the switch for a 68. I used it because the only new switches that I could easily find were all 68s, but the part concerning the horns is the same as a 65/66. The arrows are pointing to the horn contacts in the switch. The one with the yellow arrow is the one supplying power to the horns and the one with the blue arrow is the one that takes the power from the switch out to the horns themselves. The third picture is the back of a steering wheel. This is an 85 crown vic steering wheel, but, again, the horn stuff is the same. One of the horn contacts on the turn signal switch is making contact with one of the copper rings on the steering wheel, and the other horn contact touches the other ring. On the front of the steering wheel, with the three-legged horn button removed, you will see a little metal 'finger' sticking out. That is in contact with one of the copper rings on the back of the steering wheel on the back and is in contact with the metal ring on the three-legged horn button. You will also see two contacts, each made of white plastic with a little copper contact on the front of the steering wheel, held onto the wheel with a screw. In this picture of the back of the three-legged horn button I have circled two contacts on it. When you push on the horn button, that causes one, or both, of the contacts on the horn button to touch the contacts on the steering wheel, completing the circuit and causing the horns to honk.