You don't have a run a new wire to the new reverse camera, the old wire works, you do however need to add a small extension to the wire in the tailgate to accommodate the different orientation of the new camera plug.
Also inside the passenger front seat footwell, there's a kick panel on the right side where the rear camera wire has a connection before it goes to the radio. You can disconnect it there, and run a new wire back to the CVPM. At the same time, you can also run the output wire from the CVPM to that connection that goes back to the radio.
I'm sure that reads a little confusing, but when you see it you'll understand.