Glenn, the biggest thing you need to bear in mind is the 13 core has 5 thicker wires and the 2x 7 pin has 3.
I questioned this with Western towing and the only issue they told me about is the fridge wire, on the 13 pin itm is thicker. They did say I would need to use the proper 13 pin (rewire) but when I explained that the fridge in my last van is exactly the same as in the new van whats the problem, also what about using trhe adaptor. They couldnt answer!!!
They fitted my original 2x7 pin and gave me the info how to change to 13 pin.
I traced the wire back into the car kept the black wire to the o/s and ran the grey wire from the n/s to the o/s with the black. bought a prewired 13 pin socket and used connectors for each wire in the boot and then fed the new 13 pin under car and out to the towbar.
Im not good with this kind of thing but found the job easy and took no more than 1 hour from start to finish, Much better than using the adaptop imo
Hope this helps
Kevin