Are these lights supposed to be fog lights? The passenger side light comes on in reverse, so I guess they are backup lights? Drive side I can't get to come on with brakes or backup.

Any suggestions?

 

these are fog lights. if the car has the rear fog light button, then you can turn them on. the condition for them to turn on, however, is to have your headlights turned on or the front fog lights are on, i think.

 

Rear fogs for sure. I assume in the second gen MINI you can code the lights as we do in the 3rd gen cars. Mine are coded to come on as additional brake lights. You can also buy a Euro spec light switch and code the fog lights to be fog lights.
I don't know much about the second generation coding, but several threads exist talking about it.