It looks like the the DME can "signal" the IHKR to turn off the compressor so would be really good to know what module you are in when turning the compressor on. There could be something going on with the connection from the DME to the IHKR or maybe even a "data bus" issue which might be explained by rain into the open sunroof.

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