No, I think the E53s only had the pressure differential operated displacement valve so still just wire to clutch. Later, like E70 (I think) had the electronically controlled variable displacement.

If you don't have a variable displacement compressor that's not compressing then it's likely you have metal bits contaminating the system so there is that.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)