Without reading every word thoroughly, I'll wonder this; Is the horn circuit a ground triggered system, by the two constant power wires that should be the case.
The bottom two terminals are the trigger wires. From post #26, the 1 & 2 terminals trigger the relay. The 3 & 5 terminals are the controlled circuit. If the relay has five terminals, then the 4 & 3 should test as no resistance by a meter. The #4 is for turning off a circuit with the relay, or switching a circuit.
I had my 99 horn to quit, and the connections seemed poor, so I bought a newest at junk yard horn set. What I got was a 2003 Sport set, they have two wires, they actually ground the horns separate from the cases.
Test that relay well, pull the horn wire first, confirm that the relay is sending power to the horns first.