What would cause my fan not to run when I unplug the temperature censor

Unplugging the temperature sensor might have something to do with it.

Shouldn’t that kick the fan on full speed in a fail safe mode though

For testing, I'd probably jump the cooling fan relay. Note the diagram, unplug the relay, use a jumper wire on switch side of relay, right side in the diagram, cavities for terminal 30 and 87, as you can see terminal 30 is fuse protected and hot all the time. Depending on the problem, the fan should run, even w/o the key, this is just for testing. In the diagram, the cooling fan, the top wires are voltage, the bottom black wire is ground, you can use a test light to check both. If voltage and ground are good and no fan operation, suspect the fan itself. Any applicable trouble codes? Some makes and models if you unplug the coolant temp sensor, the fan will run, it's a default operation. Not sure about yours? Good luck