If you don't want to run to your lights for power, as I see it, you only have a couple of options. 1. Run it down the outside, maybe on a ladder with zip ties down below the trailer and along the frame rails. 2. Drill a hole in the trailer and figure out how to run it down the inside back wall to the bottom of the trailer and along the frame rails to the battery.
Let me be the first to ask - why don't you want to get the power from the lights?
2014 Jayco Jayflight 32BHDS
2015 Ford F250 Lariat 4x4 Crew Cab 6.7L Powerstroke