So, I read your issue with the ABS/TPS light coming on, I'm about to purchase a 2003 Mini with 32000 original miles from a friend who bought the car NEW in 2003. He decided to replace the stock tires which are designed as "Run Flats",
(meaning if you get a puncture in the tire you would be able to still drive the car for a short distance without having to install a spare)
These tires have a stronger side wall construction to the tire, but this creates more road noise when driving, so he replaced the tires with a different, more commonly fitted set of aftermarket performance tires. In doing this it caused the ABS/TPS light to come on, this only happened when he changed tire brands. Yes, you can reset the light, and it will go off, but will return because the TPS sensor recognizes there is fluctuation of air pressure in the tires because the side walls are not as stiff on aftermarket tires and this may trigger the lights, especially when the car is parked overnight. The tire temperature will be cold when the car is parked and get warmer when driven, this can cause a false alarm to the TPS and trigger a light.
Check the tires on your car to see what brand and if they're the original "Run Flats" used by BMW. If so than its likely a wiring issue or a bad TPS sensor or faulty ABS module.
A quick test would be to over inflate the tires equally for example if the tire recommends 32 psi, inflate them to 42 psi, drive the car for a few days and see if the light comes back on. I would do this right after you reset the lights, hope this helps, let me know if this fixes the problem... Cheers