Turning on the a/c should provide a ground to that third pin through a diode and several other components. I'd troubleshoot this later.

Try jumping the temp switch a on the thermostat housing like you did before. Turn the key to the II position. See if that 3rd pin gets ground on the condenser fan relay. This is the quicker to figure out why the condenser fan isn't getting power.

 

I jumped temp switch A and checked the connector. I have a ground! I then started the car, jumped the temp switch with the a/c on, and I'm not getting any power to the condenser fan. Since I'm getting all the power i need to the relay but no power out, I'm gonna conclude i have a bad relay.
Also I think the mechanic bought the wrong sensor for A, considering it never switches on. I'll do the test you mentioned for that one, to make sure I have the wrong switch then find a new one.
Only other thing I can think of what might be causing the overheating is the water pump. Not sure if the coolant's moving around or not, I'll need to test that as well. The timing belt needs to be replaced too since Lord knows when it was last replaced. I may as well replace the water pump too while I'm in there, after doing plenty of research on how to do so of course.
Seriously thank you for all of your help. You were an amazing resource and I couldn't have gotten this far without you.

 

You are welcome. That is what we are here for.

Definitely sounds like you have a bad relay. You can try jumping power from the big 12V wire to the relay to the wire going to the fan just to make sure that your fan motor is also not shot. This would be with the relay unplugged.

The mechanic could have just switched the sensors, so you may want to try swapping them.

I definitely suggest doing the water pump if you have to do the timing belt, since the timing belt job gets you to the step before just replacing the water pump.

Good luck and let us know what you find.