Don't know if that mystery wire was a horn wire, but here is the wiring for you to trace. Colors may not be accurate.
1. Black wire from horn trumpet to horn relay.
2. Red from horn relay to a good non switched battery positive source.
3. Dark Green wire from relay up thru column to horn mast bearing. (this wire probably goes thru the column connector which can be called the turn signal connector)
Your trouble can be either bad relay, missing wires or the horn button parts. obviously horn trumpet is grounded and works.
The green wire to button grounds the relay, closes it's contact which supplies the red power to the black trumpet wire.
The horn button usually pushes on a cupped/large belleville washer, that grounds the green wire to the column/wheel. you will see how that all works if you take it apart. this last issue should be easy to troubleshoot.
You can ground the relay terminal that the green wire attaches to. This will show if the relay is working and narrow the trouble.
Where did the mystery wire go after it went thru the firewall?
