you could run a switched wire (or from your truck's existing reverse lights) like mentioned above, to a relay that then turns the power on to your rear-directed fog/driving lights. you could do an easy quick-connect or a basic plug/harness concoction to make it easy to connect and disconnect when you want to. it doesn't really matter what plug you're using, or how many wires it was meant for, you will only be using one(or two).
and as for the reflectors from the housing being a bad idea, i second that as well. i personally have some LED driving lights that can just be tapped into the parking lights onto my truck. they are such a low power draw, it's a non issue. going with an led enclosure also removes/minimizes the chance of the 5-0 getting upset about a refracted beam.
something like this