I'd cut it back to the factory wires (get rid of the upfitter splice). One side of that wire should go to ground when you push the horn, the other side should go to the relay in the fuse box under the hood.
I'm not 100% sure on whether its a ground or a 12v signal that energizes that relay. I have all the wiring diagrams at work, I'll check it tomorrow.
If you leave it spliced together, go into the settings menu on the radio and tell it to honk the horn when you lock the truck with the remote. See if it works, if it does, you may have another issue in the circuit coming from the horn switch/ steering column.