Reminds me of the crazy issues I had that sound almost like yours. But in my case , among other unrelated errors with nothing to do with the alternator, I would get a consistent error "DME- 2E95 Generator - Communications loss - Fault currently present - Fault would not cause a warning Light". Replacing the alternator fixed every bizarre issue the vehicle had.

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'05 E53 X5 4.4i, '97 E39 528, '07 E92 335i, '16 F86 X6M.