It sounds like the light control module (LCM) is defective. Never had to fix mine but read about the problems. Try: Remove; terminal and earth clean and refit B4 you replace it. Also check out the wires connectors and earth points in the boot. You could find the problem or fix it with out seeing anything wrong.
Good - Fast - Cheap: Pick any two.
E23 735i; E32 735iL; E34 535i; 2 X E38 735iL (Oxford Green and Alpine White); R50 Cooper; R55 Cooper Clubman.
E21 318i; E30 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i
I've just changed my wiper blades and now my reverse lights don't work. Should I change my fuel pump relay?