I bought and installed a system like the link below (from same vendor) several years ago, and it has worked great. I did run new cables as I installed two rear cameras. In your situation, you could buy the camera and monitor with the supplied short cable, cut the ends off your current cable, cut the connectors off the new cable, and splice (solder) new cable ends to the old cable.
7" COLOR REAR VIEW BACKUP CAMERA SYSTEM REVERSE SAFETY | eBay
You can find cheaper systems, but the one in the link above seems to be good quality and has worked well for me.
If you don't want to cut and solder, then you will have to run a new cable under the coach along the frame rails. Not technically difficult, but you will be crawling around under the motorhome.
Another option would be to work with RV CAMS, and buy one of their systems. (link below). I've read a lot of good comments about them, and they have supplied adapters to allow use of an existing cable with new camera/monitor purchased from them.
RVCams Backup Cameras and Rear View Systems: Backup Camera Systems (All)