I don't have a 5th wheel, but I do have a 2010 F150 that I'd remove the tailgate to take our golf cart when towing our previous travel trailer.
Each time I'd have to climb under the vehicle to disconnect the tailgate camera. I finally decided I didn't like being without the camera when unhitched, and the tailgate is at home.
I found the wiring diagram online for mine. Your newer truck might be the same, if not, someone has a diagram online:
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I connected a cheap license plate camera to the modified stock camera connector to add a 12V plug and an RCA plug to connect. This made hitching MUCH easier, and still gave me a backup view when not towing.
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I then went a step further, put a camera on the back of the travel trailer, and would connect that cable to the modified F150 camera connector. The image below is the monitor built into the rear view mirror, looking behind the travel trailer.
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I mounted the trailer camera in the rear tire cover:
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Rather than mount the camera to the license plate, putting it near your 3rd brake light would probably help hitching your 5ver.