Sounds like a classic wheel speed sensor issue; if your hubs are rusty this will explain the persistent issue despite replacing the sensors. OTOH, my grandfather's car had the sensors go which were rapidly followed by the module.
Rear light bulbs need to be the right material for the base; copper or brass will trigger the light; the system relies on the resistance of the bulb to determine whether it needs resisting.
'99 528i ('98/12 build). 174,000km BY29428/Royalrot
Breaking My Wallet since 2009
Mods: Stoptech SS brake hose, 280piece toolkit resting on trunk floor, Beisan VANOS seals
'99 540i (grandfather's)