Has your '68 been left relatively factory original or has it seen a lot of modifications?

Have you ever heard the horn work?

Have you tested the horn(s) to see if it/they work?

When that buzzer worked, what did you do to get it to buzz?

If, the buzzer was the key in ignition with the door open, wiggle the ignition key a bit to see if you can get it to work. A worn ignition switch and key can cause poor continuity and make the buzzer fail. (I know because I am glad mine has worn so that obnoxious buzzer stops when I wiggle the key.) If you can get it to buzz, maybe it will locate the relay. Who knows, a PO may have even separated the horn and key buzzer functions into separate circuits so the buzzer might be under the dash and horn relay elsewhere.

And, as we mentioned, trace the wiring. The wire from the horn(s) and the wires to the fuse box are the important ones to trace. If the relay was relocated, the red +12v could come from numerous connections.

Do you have any photos of your engine compartment from various perspectives?