[tjts1]

You can hot wire the aux fans to check if they're functional.

 

[tjts1]

On second thought, check the big white resistor behind your driver's side headlight first. Normally when the AC is ON, the aux fans will turn on low speed through that resistor. High speed bypasses the resistor and is only triggered at 105c I think. So if the resistor is fried you won't get the aux fans to turn on but they will function when the engine is extremely hot as a last line of defense.
If you bridge the blue temp sensor on the middle of the cyl head (zero resistance) you're saying to the climate control that the engine is extremely hot (above 110c) which should shut down the AC as an emergency measure to reduce the heat load on the radiator.

The temp sensor is an NTC. High resistance = low temp, low resistance = high temp.

 

[tjts1]

You're right, the fans should turn on when you bridge the blue temp sensor so the white resistor is probably fine. Mine does anyway. Here's the wiring diagram for the fan. You can ignore my doodles in red. That was a project I was working on.

The fans can be triggered by 2 different relays so if neither low or high speed functions, then the relays are fine. The blue temp sensor is also fine if the AC clutch disengages when you bridge the blue sensor. That leaves the climate control unit (unlikely in this case since the clutch disengages) or the fans themselves. Its also unlikely that BOTH fans would fail at the same time, that leaves the wiring to the fans or the plug. Thats my best guess.

 

[tjts1]

We've established that neither low or high fan speeds work, while the AC clutch functions normally. You should be able to turn on high speed by jumping the blue temp sensor even with a failed or missing resistor. The resistor is only used by the low speed circuit and bypassed by the high speed circuit. The diagram shows that there are separate relays for low speed/AC (center left in the diagram) and high speed/coolant temp (center right of diagram). Its unlikely that both relays failed at the same time and its also unlikely that both fans failed at the same time which leaves the plug and wiring as the only common failure point for both fans at both speeds. It is possible that you have multiple failure points but highly unlikely. I would inspect the wiring and ground coming off the fans very closely. Make sure you have a good ground to the fans and check for any burnt or melted wiring.
You can test the fans by hot wiring the 12v to the black/blue wires on the fans while grounding the brown wires. You can also feed 12v to the forward end of the white resistor to test high speed or the back end to test low speed. The fans will draw almost 30a on high speed so be sure to use at least 14 gauge wire for the experiment.
good luck