I finally got around to installing the reversing camera.
After a lot of studying of the electrical schematics I found the reversing wire near the dash (instead of at the reverse light itself). I then dismantled the dash and pulled out the stereo. After wiring that up and plugging in the camera video wire (and a little more tidying up) I squashed it all back in. Most of the time for this part of the job is in getting all the wires at the back of the stereo to fit.
I then ran that cable to the rear and mounted the camera itself. It's important to have the camera in the middle so the lines it draws on the screen line up correctly. I got power for the camera from the trailer plug loom. I don't have a reverse camera on the trailer so this wire was not currently used and already had a connector on it. There was a bit of mucking around getting the cable through the tailgate onto the body, but I think I ended up with a pretty neat solution.
After a bit of tidying up if some cables I now have:
Here is the camera:
and this is what the display looks like:
Now I can hook the camper trailer up myself (thank god).