Vehicle trouble crowd sourcing.

My engine temperature gauge would occasionally peg to overheating even though it wasn't actually overheating.

It started happening more frequently.

I replaced the thermostat. No difference.

I replaced both of the sensors. Now it always reads hot, has a very rough start. Now the AC doesn't work either.

I'm going to bet that neither of the replacement sensors are bad. This makes me think that the wires to them might be the issue. It's throwing a P0117 code

Given that the AC doesn't work, that tells me it's one of the two sensors and not both. Which sensor is having the trouble?
What would you do next to try and fix it?

2005 Ford ranger V6 3L.