More than likely this is a bad connection somewhere around the bulb/holder assembly caused by overheating and/or fretting corrosion.
I just fixed the passenger side brake light on my E36 last night. The plastic bulb holder has 2 metal contacts - 1 of these had overheated and broken away. I managed to recover this one by soldering a new contact tab in place. I can't remember if the E34 has similar bulb holders but it's almost certainly a contact in that area - I haven't yet come across a BMW suffering from the more typical corroded earth contact problems.
Originally Posted by indierthanthou