I did exactly that on my previous coach, it was quick and easy. And yes, I had to have the lights on to power the camera, and I was OK with that. Well, I didn't replace the light, I just spliced in to the wires for the light. I actually mounted the camera just below the light. If you replace the light you'll want to make sure that the camera has a large enough footprint to cover the hole to keep water out.
On my current coach I spliced in to the power line for the original rear view camera. It was more of a bother because of the design of the wires in the original cable - several tiny little wires in there to work with.
On mine the original camera was not great, but it's sufficient to keep an eye on the bikes that we haul a platform in the hitch. I wanted a second camera pointed more down the road to act like a rear view 'mirror' so that I can have another view of what's behind me so nothing 'sneaks up' on me. And for the people against that, yes I do indeed use my side view mirrors, but we all know that there are people that follow closely enough that they get into the blind spot that the mirrors don't show, that's where the option of the rear looking camera comes in very handy.
2013 Winnebago Sightseer 36V