We won't dwell on what you did or how the horns are wired for now.
So from what I read on your voltage report is that all three terminal on the relay had voltage.....right? Correct
The one that should NOT have voltage is the load terminal. You say it has 6.5V........right? Correct
This is the terminal on the relay that has a wire going to the horns on the firewall......right? Correct
So since you have voltage on that terminal, it is sending voltage to the horns even when button not pushed. So that means either the mast bearing wire is touching ground somewhere inside or along the way to the relay or you have a bad relay. So now you need to put ALL WIRES back on EXCEPT the wire at the relay that comes from the column. This will mean you will have a new loose wire. It means you will have a terminal on the relay, called the switch terminal, with no wire attached because it is loose. This is the scenario I ran in the first test and the results are posted in the previous reply.
So do a voltage test on the end of the loose wire and a voltage test on the relay switch terminal (the one with no wire attached to it).
REPORT
NOW let me know that you understand BEFORE you do the test. Obviously you need the battery cables attached to the battery and obviously you need mm set the same. Also answer the questions so that I understand.
