12.3 can happen. If you tach it up and it fall back to an idle the charge will fall to lower than 13 but should recover very quickly to an acceptable range.

Did you test the battery with a load test?

When you tested the alternator was the air and lights and some other stuff on that draws juice, with X at idle for a time to see what it reads and see if the voltage bounces around?

Not implying your tests were not conclusive, just want to understand what you did.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas