1 minute ago, Shearers said:

Do I have this anywhere near right?

The terminology used is confusing to say the least. The settings for the gearbox and calibration of the gears is held in NVM (does not require external power). This can be understood in the fact that if the car battery goes flat, or is disconnected the gearbox does not forget it's settings. Unlike the electric windows.

Keep Alive Module (KAM) could be in some instances,  nothing much more than an internal battery that supports NVM.

There is and always has been a play on words regarding what NVM is. Some memory like an EEPROM is perhaps a good example of memory that does not require power. The down side is that it is not designed to be constantly erased and re-written.

@unofix, thanks for that so, for the benefit of @Morgan098 can/do we agree that (due to the expense of the internal work that looks like it MAY be necessary), the wiring should be checked in any case as it is likely almost cost free in comparison and gives more certainty that everything else has been checked before taking the box apart?
Depends also on DIY or paying someone he trusts and they need to be responsible for the eventual fix (if he says change TCM and it doesn't work, they won't be responsible, so they need to do their own check and agree?)

Checking all the wiring is always a good thing. Especially if the connection to the TCM is removed and the back shell of the plug is opened up to check the wires inside. 

Replacing the TCM is quite straight forward, no need to take the gearbox apart. So if no wiring promlems are found then that would have to be the next thing to do.