Reverse Lights Not Working

I crawled under the car tonight and noticed the connector was the original connector that has been on the car since 1974 and was the same connector on it prior to taking it to the mechanic. I pulled it off the neutral safety switch and immediately noticed the switch was different. So I grabbed the detailed invoice from the mechanic and there was a charge on the bill for a new neutral safety switch. Prior to taking it to the mechanic, I replugged that connector so many times, I was really beginning to think about gluing the damn thing on, so it wouldn't fall off again.

As suggested above, I took a paper clip, unbent it, and put each end in the outer two ends of the three prong female connector. I turned the ignition to ON, and put the car in reverse. The backup lights came on! So obviously my problem must be the new neutral switch is bad or the wrong one for my car.

I think I'll visit Advance Auto tomorrow. Did they make different kinds of switches for 74 Darts? If I remove the faulty switch, will transmission fluid leak out?