If the lighs work on the permanent on, then this is a door contact problem. This is how it works. The light unit has three wires: live, permanent ground and door ground. The live is always there, ignition or no ignition, same goes for permanent ground. This makes it possible to switch on the lights at any time. The door ground is wired so that when any of the doors open, the ground circuit is closed and the light comes on. That ground circui uses the screw in the door switch so if that screw is rusty or the switch is rusty, it will not work. I suggest you go to your local dealer and buy foor door switches, you will leave with change from a ten dollar bill. It might, I do agree, be worth checking that the switches inside the light work. Pry off the light unit and check that the metal is making contact in the light when door open position. With that light off, you can also easily check with multimetre if they get power with door open.
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George Holmer, Belgium, Europe, 1987 745 GLE Turbo Diesel Intercooler (D24TIC/M46) 200k; 1988 745 Turbo Intercooler (B230FT/M46) 290k; 1988 745 GL (B200E/M47) 190k