Seems like it could be a relay acting up, it's a possibility. When I have time later tonight I'll have a look at my Bentley manual. Truly strange issue you're having, the only other time these Mini's act strange is when a battery is on the verge of dying. I doubt it's the battery though which is why it could be a relay issue, only thing that makes sense at this point.
Have you checked out the wiring at all? If there was oil in your wiring harness....
