neutral safety switch/ reverse light unit in trans

I need a reality check. I had some problems with my neutral safety switch engaging, so I got a new one several weeks ago. Now car starts fine, but I realized that I lost my back-up lights. I put the car up and unplugged the switch at the trans and jumped the outer two sockets in the wire plug and the back-up lights come on. I think this means that the back-up light part of the switch is faulty, CORRECT???