neutral safety switch/ reverse light unit in trans

Did it ever work correctly?
I don't think so. I was so focused on the starting issue that I didn't even check the back-up lights when I installed it a several weeks ago. Now the car starts every time, but no back-up lights. Since they work fine when you put in a jumper wire at the trans harness plug, I assume that the only issue has to be the switch or how the switch is activated inside the trans, correct?