2006 X5 3.0 air conditioning diagnostics - looking for some guidance/roadmap

[fiataccompli]

The AC stopped working on my wife's car last week. It's particularly poor timing as she's using it to make long trips at the moment to care for her father who has had a stroke & is in another state. Such is life. Our X5 has been a reasonably (actually well) cared-for vehicle and has given few real issues, but it does have 174K miles, so I expect things to break.

A cursory look at the AC seems to indicate the compressor is not engaging,
(belt turning, hardware on front of compressor is stationary) but connecting a gauge to the low pressure port shows high pressure (sorry, I didn't record nor do I remember what, but it did NOT read low). I think the aux fan is engaging as the routine test upon startup & it does engage when the connector at the high pressure switch is removed. I replaced the aux fan last year (symptoms were a few cooling system overheats and AC only worked when the vehicle was in motion) and I bought the hardware/software to set up a dedicated BMW scan laptop for her car at the time.

I don't have a full rig to vacuum the system & I'm not looking for a quick 'hack' to get it going, but as a lifelong DIYer, I would prefer to do as much of the initial diagnostics as possible & obviously (I suppose) if there is a simple fix that does not involve opening the refrigerant system, I'd most likely do that myself if I could ID the cause.

I have not checked fuses & have not checked any other electrical connections for fraying, wear,etc.

I'm assuming the next step is to see what the scan tells me. And, I'll assume that I'll be able to translate what it tells me into practical terms.

Is the compressor on this model one that can be simply/viably tested for + voltage w/ the AC on & even be jumped to test whether it's mechanically functional, or is it controlled via pulse signals like the aux fan?

Any other no-brainer checks someone may want to share from experience would be welcomed.

Any pointers to a system overview/exploded view/etc. online documentation of this AC system would be helpful of course also (I've only found various forum threads so far).

Thanks in advance.

subject vehicle: 2006 X5, 3.0 174k