No horn. Only get 6V at the wires. If o disconnect it, I get 12. Is there a relay in circuit? Anyone know where it's located?
Reading voltage but low seems like a connection going bad. May just be the horn button. I would start there,
OR,, the horn is bad and pulling B+ down. Put a light on the leads with horn disconnected and watch if B+ stays up or drops. If it drops, start looking for a bad crimp. You can always jump the switch with a screw driver to check there.