[Citroënbender]

I presume you mean the cabin fan?

Many have a thermal trip on the controller module, if current draw is excessive (due to worn brushes, stiff bearings) it will shut down - which does block the compressor clutch engagement signal.

Other stupid designs I’ve seen energise the clutch coil by a solid state relay on the climate control board or body module. Great theory, fails in practice as loads exceed design specs.

You really need to view the live parameters to see what the controls think they are doing or reading. Actuator tests are also handy.

To be fair, most systems can be reasonably diagnosed via experience but the presence of a less common fault or inadequate previous work may complicate.