Sounds like you are talking about either the 5th gear switch, or the back up light switch in the tranny. Neither are required for the engine to run properly.
I don't remember, off the top of my head, which switch has which connector end on it (one is male, one is female though). I guess if your back up lights work, when you put the tranny in reverse (with the key on), then it is the 5th gear switch pigtail, that you are talking about.