I don't know if you missed anything, but I would be isolating parts and working backwards instead of using the system to check the system if that makes sense.

so your first check is the horn works.

now back up to the relay.
or rather wiring from the relay.
use the jumper to supply power to the horn from the relay wire to the horn. Make sure that is still good.
if the horn sounds back up to the other side of the relay power supply.
to do that though you might unplug the horn ring ground and wire up a wire to ground the relay from where the horn ring would have done it and see if the horn sounds.
if it does you back up to the bulkhead connector and see if you can ground it from the outside and then the inside, etc..