Well, I wired our 2009 Honda CRV so we could tow it 4 down. However I did not use the bulbs as you indicate you are going to do. If I understand you question, you have bulbs you are going to install in the Honda tail light housing, correct? If so, you don't need to worry about the original Honda wiring. From your motorhome trailer plug you will run a taillight wire, a right stop light wire, a left stop light wire and a ground wire all the way back to the new bulb sockets. You will need to drill a hole in the rear lighting housings to accommodate the socket and bulb making sure the new bulb does not hit anything inside the housing.
On my set up, I also ran a 12 volt charge wire from the coach to the Honda's battery. That way I did not need to remove any fuses in the Honda, and the Honda's battery stays fully charged. If you do this you will need to provide a ground wire to the battery also.
BTW, I also installed the Blue Ox base plate, and I also had many more hours invested than Blue Ox led me to believe it would take.
I am not familiar with the Patriot Brake system and its wiring needs. I installed the M&G Engineering Brake System in the Honda.
Good Luck, Be Safe and Above All, Don't Forget To Have Fun
2006 Fleetwood Discovery 35H, being pushed by a 2009 Honda CRV