Hi Mike
This may be of no help at all as I can only describe the set up on a 2002 36C which is much simpler in that it has separate battery and fuel meters and just one toggle switch.
The toggle switch has 2 inputs from batteries 1 and 2 and one output which goes to both meters and there is no driver circuit as such on the board. When both batteries are switched on both meters and their back lights will work with the toggle switch in position 1 or 2. If say battery 2 was switched off then neither meter or the backlight will work when the toggle switch in position 2.
With 3 toggle switches on your 360GL the set up is much more complicated. Not sure how it works. When measuring the battery voltage do the other 2 toggle switches need to be in the off position?
You say the backlight is working but is this the case when it is in battery measuring mode. If yes then that suggests that power is getting to the meter and that the switch is ok and the problem may be with the meter, which given that it works in the other 2 modes is highly unlikely. If no then perhaps there is a problem with power getting to the switch or the switch itself. Are you able to measure whether there is any voltage at the input terminal to the battery toggle switch?
Of course, 20 years on and electronics have become a lot more complicated and your set up may well involve a driver circuit/PCB on the VDO board. In which case the above will be of no relevance at all.
I would agree that the Dufour manuals are pretty useless but they are better now than they used to be.
Hope you get the problem sorted.
Andrew