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.
3 x E32 735iL (Alpine White, Glacier Blue & Kashmir Beige); 2 X E38 735iL (Oxford Green & Alpine White); E53 X5 4.4i (Pearl Beige); R50 Cooper; R55 Cooper Clubman (Both Pure Silver).
E38 Parts Car
E21 318i; E23 735i; 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?