According to my 1992 service manual (most C4s are similar) the horn fuse is located on the right hand end of the dash near the passenger's door. The fuse you are looking for is a 15-amp fuse labeled THEFT. The steering wheel horn buttons activate a horn relay located below the right side of the dash just above the bottom cover (knee bolster) near and below the back of the fuse cluster. This relay simply closes the circuit between the fuse and the horns. The relay is also triggered by the Central Control Module for use by the Security System, but that probably won't be a factor in your problem.
The wire color between the fuse and the relay input is orange. The wires from the relay to the horns are dark- green color, and go through just one connector C100 located in the left hand side of the bulkhead connector into the left engine compartment. Finally the wire from the horn buttons to the relay are black and pass through the C204 connector located on the right side of the steering column.
Check the fuse first. Then activate the horn button and listen for a clicking sound from the bottom of the right side of the dash. If that clicks then the problem is between the relay and the horns, probably at the bulkhead connector. If there are no clicks the problem is most likely the relay itself or the orange wire connection to the fuse. That's about all there is to it. As a C4 owner I know that NOTHING in the dash is easy to fix. However the factory service manual is absolutely essential in doing any repairs of a C4 Corvette. I hope this is the help you need.
Good luck my friend. . .
Merlin49
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