While the carburetor may be less than perfect, there is plenty of evidence of an electrical fault.
Idles in park just fine. Once you move the column mounted gear selector, "Trouble Starts". The horn does odd things. Turn signal may be affected.
Time to start looking at the wiring in the area of the column assembly. Perhaps the shift linkage is contacting wires in Drive that it does not touch in Park. Maybe the steering shaft is rubbing on some wiring.
A weak short to ground can trip the horn relay. Such a ground path can be established by shorting the horn wire to a turn signal bulb - which is grounded on the other end of the filament. As the filament heats up, the resistance goes up - eventually far enough for the relay to turn off.
Disconnect the wires at the ballast resistor. Set the parking brake. Reconnect the horns. With the ignition on, put the car in drive. Wiggle test the gear selector, turn the wheel. Try the turn signals. Try the horn.
If you get the horn honking on it's own walk around the car looking for a bulb with a dim glow.
Crawl under the dash with the selector in drive & look for contact with wiring. Look in the engine bay as well.
Pulling the wire off of the horn just hides the symptom. Wiring faults do not get better. They can get worse, and usually do so in spectacular fashion. You can burn a car to the ground with an electrical fault.
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