Not entirey sure here but if yours is P reg V8 then it should have a hot oil cooler in the radiator and a cold oil cooler ahead of it, the "bog brush " or "hairy sausage" type seem to have been superceded by a long flat vane type around the mid 90s.
Wires on the back face of the transfer box are the T-box oil temp sensor, LHS of the T-Box is the speedo pick-up, front left of the gearbox is the inhibitor switch/reverse light switch. The auto box heat warning sender is at the front of the engine bay.
But it might not be the gearbox at all. try bypassing the inhibit switch, the wiring drops down at the back of the engine bay.
BTW, your selector should slip between "3" and "D" without pushing the button, this is indeed to allow you to hold 3 when towing, I do it with my LSE to allow the engine to rev rather than labour. 3 is also the most direct gear. You shouldn't need to manually select "1" or "2" though, your more likley to damage to box in time by shifting too late. (if you shift early it won't change gear, either going up or down).
The ZF only has position "1" for off road (the same gearbox in a car doesn't have it at all), it locks an extra clutch to give engine braking downhill, otherwise you off-road in "2", "3" or "D".