Issue resolved. I ended up having to take it to the engineer who services the car. He did say to me to check the fuses in the boot which were added to the battery after manufacturing. This was the very first step I took. The pin layout I have checked and also it is printed on the cover of the socket, so I was pretty confident of the layout. Having checked the fuses on the battery with no success, I ended up checking every other fuse in the engine bay, of which there were many!! Still no success, so a visit to Gary. After an hour he came back and found the issue. He managed to trace the cabling of the socket (something I was not able to do) and found the connections added at install. He then checked all the fuses and found one was actually missing. When he fitted this, the power was found to switch to the pin when the ignition was on. Now this was confusing, as I believed I had this before the cable change on the caravan. AS the cable was changed independent of the car, I cannot say it was removed when the did the work. All I can now assume, is the power was never there in the first place. Gary charged me a 1/3 of what Lexus were offering. As a note, I did contact Lexus in Reading and explain the circumstances and received a response.
Thank you for your email
I have checked in to the tow bar fitment on you NX300h and can see it was fitted back in October 2016, we would have advised that as the tow bar was fitted two years ago that there would be an initial diagnosis charge of £185 + vat, if at this time we found that the fault was due to the original fitting of the unit we would have corrected the fault with no charge to yourself, as you declined this and the fault has been corrected by a third party I am sorry to inform you that we do not cover the costs of any third party repairs
The only advise at the time of speaking to Lexus was to offer to investigate at a fee of £185+vat. Nothing about FOC if found to be their mistake. I wonder also if they would have "found" the same issue. One will never know.
Thank you for your responses and help Neil, it was appreciated.