Did you replace the coating on both sides of the pickup ring? Remember to coat the inside of the hole. The ring has to be completely insulated from any grounds except the horn button.
You can test the ring with the use of an ohm meter or buzz box. Put one lead on the contact surface and the other lead on a bare metal section of the can. If you get a meter reading or a buzz, the insulation is not working and the horn will blow all the time.