I had this sort of problem on my Fiesta - there was dirt and corrosion down inside the connector socket - after cleaning - things that had not worked previously showed signs of life.
Foolishly I first tried cleaning it with a metal file and popped the 10A fuse (idiot) - screwed up sandpaper might have been a solution but I was able to give it a good clean up with a pointed Dremel stone.
I think the piece in the middle at the bottom should ideally be shiny brass.
