OK, I dug into these over the weekend. The previous owner wired these lights in parallel with the lights shown immediately above the fogs in the picture (specifically the smaller side bulb inside the light). Since those lights (I think they are parking lights) work, I'm guessing the bulbs on the fogs are burnt out. Unfortunately, they seem to be extremely difficult to get to in order to change them.
Also, the lights appear to be very poor quality. So, I'm not sure it's worth the trouble to put the effort into changing them. I'm thinking I should rip them out and replace them with a factory set and new switchbank. I understand this will be fairly technical, but I think it's the best way to proceed. Thoughts?
PS. Here's a link to another thread, in which I posted several pics of the vehicle. Let me know what you think...
MINI COOPER :: North American Motoring - My first Cooper S