After removing the plastic access panel below the bumper, you will see how the fog lamp housing opens up in the rear to facilitate lamp replacement.
On my W210, the problem was the wire into the external junction was corroded and had broken. I simply stripped back to clean wire, soldered it into the connector pin, and all is well now. I guess you could remove the little junction completely and use a insulated male/female spade set.
Best Wishes,
Ron