My guess is that the affected bulb socket is bigger (looser) than it should be and the bulb does not maintain good contact. If it is a plastic socket with power and ground contacts for the bulb, you might be able to bend them slightly with a dental pick or similar tool.

When I had my first Mini back in 1972 or so, I had the same problem with a tail light. One very late night I had a police cruiser pull into the driveway right behind me. His reason for the 'stop' was the out tail light. I explained about the loose socket and 'fixed' it in front of him with a single slap to the Mini's rear fender. He wanted to know where I'd been so late - I had a good alibi - as there had been a break-in somewhere in that end of the city. He wanted to see in my Mini, a Countryman (wagon} so I obliged. It amused me to watch him try to see under the Mini seats with his huge police-issue flashlight. He eventually spotted the fishing tackle box under the rear seat and wanted to know what was in it. "Tools!". I popped open the rear doors, knelt on the cargo floor, reached over the seat back, flipped up the seat, pulled the toolbox out and flipped it open for him. 'Tools."
He was satisfied. I really think he was bored on a quiet, dark night and needed something to do.

Different times!

I added a brass shim to the socket to take up the slack.

Have you tried removing the tinted light assemblies and try the original light assemblies? If the problem goes away, I would suspect the tinted light assmeblies...

Hi All, recently fitted tinted rear light assemblies to my 2007 R56 mini cooper D. I changed original bulbs to 500 Lumen LED for extra brightness. But now i have an intermittent fault on NS tail light upper lens. sometimes reacts to a tap on outside of lens. i've tried putting original bulb in, removing complete assembly & cleaning all contacts, but no success. i've yet to try a fault reader but this seems only action to get satisfaction. any advice gratefully received.