2003 X5 3.0i Air Con won't engage

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I am in UK and have a 2003 X5 3.0i with an air con issue I don’t quite understand.
Worked O/K last year, this year system has just been re-gassed by garage who said I have another problem as the compressor won’t kick in. Green light/switch on centre console seems to work and fuses all intact.
Plug connector (big + - wires) to condenser fan shows 12 volt “all the time” even when Green light/switch is off. Fan is not seized and reads some electrical resistance but will not turn, so this looks suspect but expensive for what it is.

Not sure what the third smaller wire does on the connector either feedback or drive the fan in some way? If fan is not turning the third small wire could feedback into vehicles brain which in turn will stop compressor engagement. However it may drive the fan unit in someway I have yet to understand. but I do not understand why there is 12 volt “all the time” on the fan supply as this suggest it will burn out any replacement.

Have I got another deeper problem, and can anyone add more information on how it works.