[jimh]

Well, with new switch - the problem is exactly the same. Back to square one.

Sequence is:-
Cold start.
Ignition on, warning lights such as battery light illuminate immediately.
After about 2 seconds, the speedo, tach & DIS light up and the fuel gauge goes up.
At this point only "P" is lit on the DIS.
Crank engine, cranks for a couple of seconds (appears strongly) then starts.
As the engine starts, the DIS immediately lights PRND432 (about 1 in 3 times at the moment).
PRND432 stays lit and only reverse and 4th gear are available until I switch off and restart. On restart, it works perfectly every time.
It works perfectly every time if the engine (or the weather) is warm.

Cleaning the F125 switch or replacing it makes no difference at all.
Switching on ignition, then shifting the gear lever all the way down to 2 and back up to P before starting seems to make it work properly every time (this convinced me the switch was at fault).
I have had the gearbox control unit out previously and cleaned / inspected the connector. Also opened it and inspected the PCB for dry joints etc.

Tomorrow morning, I will take the laptop out to the car with me and pull codes while in the error state (if it happens), as no fault codes are being stored.
I'll also do a load test on the battery.

Is it normal for the warning lights to light immediately when ignition switched on, and the rest of the dash power up a second or two later?
Car is 2001 FL.