Jaguar X-Type radiator fans don't come on when expected.

I have an X-Type from 2001. The cooling fans don’t come on when the motor runs hot or when the AC is on max.

I performed the check described in the workshop manual, which is to connect the control module to a 100Ω resistor instead of the temperature sensor, and then the fans do come on. So the fan itself is fine and the cooling module does trigger on extreme heat, just not on normal use heat.

Can this still be the well-known faulty cooling module issue and should I find a replacement module? Or should I look elsewhere?

(I did consider the temperature sensor, but since the dashboard temperature gauge does indicate the right temperature, that seems unlikely to me, or is it?)