Ok look
This is the switch. The single green wire is for the gauge. If I disconnect it, the needle drops to 0. The 2 other wires used to be in a connector I guess, but now they aren't anymore. I got one black/green wire and one black/blue wire, which corresponds to the wiring diagram in the manual. And I guess the switch pictured above is the one circled in red in the diagram below:
According to this, if I bridge the black/blue wire to the black/green wire I should power the fan clutch. I tried this, but when I do it the wires spark and the jumper wire get really hot. What am I doing wrong? Do I have the right wires?