my back-up lights don't work!

I began trouble shooting... jumper wire on the plug for the switch, and the lights come on like they should.

hook the wire up, pull the switch out, push the ball in...nothing.

Ok. I need a new switch.

few days later when the Rock Auto box arrives...same thing. but this time, with the wire harness plugged in, and I push the ball in on the switch, the reverse lights come on. but installed on the trans and in reverse gear...nothing.

I tried to look inside the hole with a mirror, and when in reverse I can see what looks like a square plug that is what's supposed to push in on the ball of the switch to turn on the reverse lights. When in reverse, I can see it with a flashlight and a mirror. when I shift out of reverse, it goes away.

how do I fix this or troubleshoot it further? is this a common problem? do I have to pull the trans to figure this out?