The magnetic clutch as upallnight has described can also explain intermittent AC function. Even if 99.5% of the time those symptoms say the compressor is shot:

1) you are flying blind without the tool to tell you what's what
2) the tool will for sure confirm you are correct when you can verify the compressor is not compressing until it wants to
3) you will definitely want the gauges if the compressor is shot because you'd be foolish to risk hurting a brand new compressor flying blind without the right tools.

So, yes you might be 99% on with just the overnight diagnosis but you'll be 100% when you confirm with the right tool.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)