ok, so, just to be absolutely super sure, you checked the connector labeled number 2 in this photo with the lights turned on and you grounded the connection to the black wire on the cigar lighter connector and you read absolutely 0 volts?? (ignore the random number 2 and the messy state of my Range Rover, this photo was taken just after I got it and I was fitting a speed camera detector, its now all clean
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In that case looking at the electronic troubleshooting manual I would suggest theres a fault somewhere along the wire, possibly at S612 which is a 'wire-to-wire' splice.
The diagram below shows what I am on about. Have you had any trouble with the gear shifter lighting or anything as that aspect of the lighting is on the same circuit as well as you can see below.
The next thing I would do is to check you are getting 12 volts out of the BeCM. You will most likely need to remove the drivers seat to do this. You will then need to check pin 11 on connector C625 on the side of the BeCM - the side of the BeCM closest to the centre of the vehicle.
The wire that comes from pin 11 is RED and BLUE. When checking the voltage ground the voltage tester at earth point E621 as shown in the photo at the very bottom - this is where the circuit is earthed in the end, not only that it will be right next to you and within easy reach.
DO NOT unplug the connector with any sort of ignition on. You dont want to risk upsetting anything.
If it was me testing I would turn the ignition on to stage I after removing the front seat. I would then turn the side lights on and slot my positive probe into pin 11 of the connector, this should be enough to make contact with the actual metal pin itself. If you cant reach the metal pin with your normal tester, turn everything off and remove the key and slot a straightened paper clip into the connector making sure its touching nothing else but the metal pin and then try again using the paper clip as the point to test voltage - Ive used this technique several times and its always worked perfectly. I then would just ground the connection at the earth point I mentioned earlier.
This view is of the connector as though it was plugged into the BeCM. So when you come to test, pin 11 is along the bottom towards the front of the vehicle.
Im hoping with the lights on you should find 12 volts coming from the BeCM. In which case you will know you have a problem somewhere along the wiring to contend with. If its not 12 volts there maybe something more serious to contend with. I would try the above test before anything else though. Sorry for the long rambling post as well, just trying to make sure everything is fully understood and you dont end up hurting yourself/blowing up your Range Rover/setting fire to next doors dog etc etc
Good luck and post back with results.
-Wills