Can't answer your question directly, but can tell you what I did on our '07 Wrangler. I rewired one of the dash 12v recepticles so it is powered through the tow harness (same as used for the tail/turn/stop lights) and installed a blade switch on the negative battery terminal. The brake is now powered from the motor home.
Jay & Peggy Monroe with Dolly
Can't take it with you - don't plan on leaving any behind
2016 Newmar London Aire 4553, Spartan chassis
Wrangler Unlimited toad