I cant recall, for 100% for sure, but I believe the wire you speak of was a ground wire.
I think the 3 prongs represent
12 volts in
5 volts out
Ground
Seems to me if you get continuity between all 3 prongs you have a switch that has failed in the closed position and will deliver 12 volts to the gauges.
Someone smarter than me will tell you if I am stupid.
