Horn Tech Question

No idea. Here's what I'd try. Unplug the relay. Hook a test lamp to the black wire at the connector. Hook the other end of the test lamp to a "hot" battery source.

The lamp should light when you work the horn button, either key on or off.

Might be the column is not grounded, but that's only a wild guess

Any wiring mods you know of?

Any harness "meltage" from other damage / shorts you know of?

Is the wiring factory?