I have a 2012 Countryman All4 and the rear brake lights remain on when the head lights are on.
The hatch brake light does works when brake is engaged but just at partial brightness.
I have also changed the brake light switch and there was no change in status.

I then disconnected the front (stock) headlights to see if there was some feed back no change in status.

Then pulled both rear light clusters to check the bulbs and they appear ok? Problem persist...

A clicking sound can be herd elsewhere when the contact plate on pedal lever moves from the switch plate.