not quite sure. I will pull a C3 one from a local yard and pull it apart to compare. I'm curious about this myself. A new switch for me would cost about $80.00, but it IS a motorcraft switch. However, I don't have that cash to spend, and like you, I have no backup lights.
I got my switch reassembled and all the wiring tests out okay. I will know next week if it all works properly.