Can you plug the left or right camera in the back camera port. This would tell you if the camera or interface is bad.
Can you verify the back camera is getting 12 power?
Maybe there is an interlock such as a reverse signal that needs to be energized and is not.
Can you post a wiring diagram from the manufacturer?
06 Hurricane 34FT WH W20 Chassis 8.1L 129K, Steersafe, Koni Shocks, DIY Trac Bar, Tri-Metric 2025RV Battery Monitor, 4-6V Batteries, Scan Gauge 2, Crossfires, 735W Solar Morningstar MPPT-60, KVH R5 In-Motion Sat, XM Radio, 07 Chevy Malibu Maxx Toad, Falcon 2, Brake Buddy, Escapee