Jughead, many thanks, much appreciated. This firms up that the problem is most likely the voltage drop. I have already removed the plug and sprayed CRC on it, there was no corrosion however so that was a long shot. I have a BMW manual on a disc but it contains no circuit diagrams, have ordered a clymer manual that has circuit diagrams, should have it this week. Will then trace the high resistance joint. Worst case I will get an alternate supply from somewhere else but need to see the circuit first.
Thanks again for taking the readings, it gives something firm to work with.