I'm no expert, but I think it would just be easier for you to go to your local parts store and pick up a new wiring harness for a trailer and just tap it all into the existing wiring for your rear lights.
I did that on mine because when I got mine, a couple wires were broken, and the plug itself had been drug on the ground for some time and was ground down to just about nothing. So, off with the rest of the wires up to the body, and just got a new plug and just spliced into the tail lights. Funny enough, a couple weeks later I was moving and the trailer I borrowed needed a 7-pin plug, so I had to get an adapter, but it works like a charm!
I did that on mine because when I got mine, a couple wires were broken, and the plug itself had been drug on the ground for some time and was ground down to just about nothing. So, off with the rest of the wires up to the body, and just got a new plug and just spliced into the tail lights. Funny enough, a couple weeks later I was moving and the trailer I borrowed needed a 7-pin plug, so I had to get an adapter, but it works like a charm!