First of all, you need to make the distinction between "back-up camera" and "rear observation camera". The mount on the back of your trailer is for a rear observation camera. A back-up camera usually goes in your license plate frame or thereabouts somewhere. Your trailer is pre-wired from the rear camera mount to the umbilical cable that attaches to your tow vehicle. That's where your camera gets it 12V power. It then sends a wireless signal to your monitor in your tow vehicle, which gets it's power from a cigarette lighter receptacle. There is better and cheaper units out there than the Furrions; PM me if you would like the name of the one that we bought. Ten minute installation.
After you've done all this and it doesn't work, remember to turn your lights to the on position to power up the camera. Not auto, not daytime running lights, none of those. The lights have to be in the "ON" position. Good luck to you!