I have an 87 635CSi. The low beams are the outside bulbs, and normally when the high beams are switched on, the low beams switch to high beams and the inner lights also illuminate, so there are a total of 4 headlights on....until about two weeks ago.

Now, the low beams behave normally, but when the high beams are activated, the left outside light turns off, the left inside comes on, the right inside doesnt do anything, and the right outside switches filaments from low to high. So basically only half the high beams are working.

My guess from working on Nissans is something with the headlight switch, but I am fairly new to BMW and have noticed that German electrical systems are unlike any other.

any suggestions please?

Do you have a wiring diagram? You may need one to locate certain components and test points during the tracing of the wiring.
If I recall, there is a multi-pole relay that performs this "switching" function for the headlights. There is a possibility, (if you do not have any damage to the wiring), that one or more of the contacts in the relay have become fouled with carbon arcing.
The only reason I mention damage to the wiring is that I just had a 5er come into the shop with certain light fixtures not working. After tracing wiring and checking voltages at the test points for about an hour, (the failure of the light fixtures followed no logical pattern), I was forced to begin to trace out the wiring harness inch by inch. Found rodent damage to the wiring harness in a place that would not normally be seen by overall visual inspection.
andrew

Have you verified voltage at the bulbs?