[wozz]

Does having the trailer plugged in disable the reversing lights on the vehicle? If so I'd be checking around the socket for a broken wire? Or is it just a parallel circuit?
What voltage are you getting at the bulb-holder?
Have you checked all of the bulbs for continuity (yes I know it's basic and the chances all going at the same time are slim if 2 bulbs to none if 4 bulbs, but still...)

 

[wozz]

Replacing the loom may not have restored everything to normal. I'm not convinced that the manual will help with the 13 pin socket, Presumably there have to be some breaks made in the original wiring if functionality of the vehicle lights is affected, and putting things back to normal just loops the original connections back to where they were before the socket was fitted? (I'm guessing here), but that's where I'd start looking for continuity.
Can you identify the pins used for the reversing lights

 

[wozz]

noooooo..... famous last words...I'm going out to fix the car I may be some time...
getting pneumonia isn't included in the fix, leave it until it's warmer.
The wires are colour coded, hopefully someone will be able to tell you the colour of the RL wire(s)? so you won't have to take off the cluster
I don't do cold unless I'm walking as I lack insulation and I'm a wimp so you have my sympathy

 

[wozz]

The ultrasonic sensors only need to know when it's in reverse, same signal, afaik separate a wire is not required.

 

[wozz]

That's a different issue, the sensors don't care whether the bulbs are lit, only that they are enabled to be lit. (is my take)

 

[wozz]

The diagram doesn't show if it's a make before make, doesn't the switch only know one or the other position, there isn't a third position is there? I assume all connections happen at the same time? You don't need to remove the switch to check it, your meter should tell you, presumably all pins short when operated? (Unless it has 2 positions which I doubt?) (change of mind see later)

 

[wozz]

On reflection you're correct, why would they go to the trouble of fitting an extra pole if they both made to the same common at the same time, it wouldn't make sense..I retract my last post.

 

[wozz]

Great result and I admire your tenacity.
Doesn't pressing the clutch tell the CC to stop?
So under normal driving use is the switch is as shown, relaxed?
Does the switch have 2 working positions depending on what gear you're in or is is momentary? (I'm asking because of an earlier comment about difficulty in setting it up).
It looks from the photo that one pin should always be connected to chassis? (the LH as shown).