Bulbs mounted in plastic have ground wires, bulbs that have a metallic path to ground may get their ground through their mechanical connections to the body, etc.

Make up a jumper with clips of the size needed (ie large one to clip on bulb socket if possible) and ADD a ground to each bulb to see if that changes things.

This would get around a broken ground wire where you cannot see it. If this works, just add a permanent extra ground.

On our '88 745 GLE we had a headlight out - my daughter changed the headlight to no avail. I checked for voltage and found 12 volts. I changed the plug to the headlight - still no light.

I stripped the wires back about a foot and found that one wire was full of black gunk and only had one copper strand left! The light was on, but not bright enough to see it.

I went to the pick and pull and obtained a used plug with wires all the way back to the firewall and spliced in to our car.

I would pay more attention to the front of the car as the wiring is exposed to more salt, chemicals, etc. than the rear is.

A wiring diagram does not tell you where the wires run.