Fuse in aux relay box on E34 1988

Hello all,

My car is E34 1988/08, with A/C, climate control and independent heating system.

There is an auxiliary relay box with healights washer module, 3 other relays, and one fuse. I have noticed that the fuse is blown.

I have tried to replace the fuse, and see what unknown feature will start working :) However, the outcome was really unexpected - I could not shut off my engine! I mean I was able to take the keys from ignition switch and the engine was still running. The only way to stop the engine was to remove the fuse.
I did more reasearch on this, ant I've found out, that the engine would run (and A/C too) with the key in position 0 or 1, only when lights are swithed on. If I move ignition key to position 0 or 1, engine stops only when I turn off the lights.

I think, that some "smart" mechanics has done something stupid with electricity on this car, but I do not have much ideas what to check.

I think it would help me a lot, if anyone could say what this 5A fuse in aux. relay box is responsible for?

thanks for any ideas,

g.v.