OP: Not butting in, please stick with Koalar's diagnostics.
@koalar It also checks status of brake switch - Dodgy brake switch or burnt earth connection to o/s rear light can puzzle it (amongst many other things) without giving obvious symptoms.
It would be fairly easy for an auto electrician to eliminate the sensors by measuring the control side of the inhibitor relay and seeing if it's commanded
Or temporary bypassing it altogether, which is where I would start, not so easy to advise on a forum from a safety point of view
Have to wait until the OP gets back, and see if there's any hints in the video
Got to be a clue it works fine if the outside temperature is low, but it's not something I remember coming across this way before, and has me scratching my head at the moment