I see 13.8v-13.9v. This reading is a little lower than the measured 14.1v-14.2 at the jump terminals but this difference seems to be consistent across most variants (of E53).

Yeah, if you see it dropping to below 13v, your alternator (or rectifier/regulator - part of the alternator) is very suspect.

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Wayne
2005 BMW X5 3.0d (b 02/05)
2001 BMW F650GS Dakar (b 06/01)