I added the side camera's to my Montana after Christmas this year. They were my Christmas present. I did some YouTube video watching and picked up a couple tips which changed the direction I intended to go with the side camera's.
First, one thing that became very apparent was the view from the camera. By putting the side-light/camera in their original position by removing the old ones (up front), the door trim from the propane tanks would block a portion of the view. I picked this tip up from YouTube. I did pull one side light out and put it in place and tried it, and sure enough, the trim on the door blocked too much of the view. Plan B was born.
I decided to just leave the originals in place and I raised the new yellow lights up high enough the propane gas tank doors would not block their view. That meant drilling a new hole for the wire to go through, applying some adhesive, and screwing the new lights/camera on carefully and in a new location. The end result was fantastic! When traveling, nothing blocks the camera view now.
Of course, this meant I had to splice into the existing wires, which was really very simple to do. I wired mine so the camera would be active when the running lights were on by the truck:
Your's should be the same, but my lights had 2 sets of wires coming out of them. One set was for the amber light. The other set was for the camera. This way, both sets could be connected together so both camera and light is on at the same time. Or wire them independent with a different power line to the camera and then you could toggle the camera on-and-off independent of the need for the tow vehicle to be attached.
I am thinking your situation is very easy to fix. You need to open the light/camera from the back, and you'll find the second set of wires for the camera. Attach them together and they'll run off your truck when plugged in.
You REALLY might want to think about where you place the light/camera. I looked at some images of your camper model, and you will also have blockage of the camera view if you mount the new camera/lights right on the same spot where old amber running lights are located.
Good luck!