If the Dark green wire coming out of the firewall is a AAW wire, it is on Sheet 1 of 500558 instructions. As per instructions, install terminal style "E" on to wire, snap it into connector "J" and plug it onto the terminal on the horn trumpet. Sheet 2 shows this Dark green wire coming out of the connector on the drivers side of firewall. (see conflict note below)
Now go to 500560 instructions for the other two wires. Find the relay on the diagram sheet 3. One is a black wire shown to/from the column connector. This goes up the column and to the upper mast bearing slip ring. you probably have to splice to that existing wire. This is the "trigger wire".
The other wire is the "Red Hot" battery supply wire. It is shown coming from the fuse panel. I assume you have a red wire coming out of the fuse panel you have not connected. The old red wire to the relay should be removed and replaced with the proper AAW wire.
Note: I may see a conflict with 500558 and 500560. Not sure yet,
Did 500558 come inside the 500560 kit or was it purchased separately? Did you buy the kits or did they come with the truck? Was any of it already installed by someone?
That pic looks like a horn relay. The relay you want is
here. Where did you get that relay?
Sure hope your battery negative cable is disconnected during all this.