Hey guys,
I was able to get the switch out, and back in. I'm actually not bad at it now.
The little spring inside the switch was bent way over and contacting the bolts that hold the thing on, making a constant ground, thus causing my reverse lights to stay on. At least I assume that's what was happening, because when I looked in there it was bent way over against the bolt.
I put the thing back on, and no reverse lights. I took it off, shifted into reverse and felt around up there to make sure the contact is coming out, and it is. So after twisting the lead around to situate it and playing with the spring, I can't get it to pass current through between the spring and the lead on the outside of the switch (I checked with a volt meter). I get 100% resistance when I put a voltmeter on it. That spring is super flimsy too. Seems like it's waiting to fail. I'll mess around with it some more, but I'll likely just order a new switch.
The great thing about all this is that this is fixable. I was worried I'd get the thing off and there would be some other issue.

