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After consulting my '66 shop manual, it seems that the horn circuit doesn't have a relay, at least in the stock '66. I still think maybe the circuit may have a short somewhere if the rings are sparking. Does the horn honk?

I did put an after market relay in my car that operates the horns because I just had low voltage in the horn circuit. I used that to operate a relay that shot full battery voltage to the horns when operated. I did that because I wasn't getting enough voltage before that to reliably operate the horns from the original circuit. Look for a short in the circuit. If none is found, you could do what I did and just use the orginal horn circuit to trigger a relay that operates the horns.

Rev