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Arief, A battery at rest (a couple hours after its been charged) that measures 12.1-12.3 is between 50% & 70% charged. 12.1V equates to 50% state of charge (approx). The voltage while your engine is running is the alternator voltage which should be between 14 & 14.6 or so depending upon whether its charging or just supplying bus voltage.
Since you guys are in the middle of summer down there (or at least in the warmer months) I would say your battery is all but shot. Batteries go bad in the hot months but don't show themselves until it gets cold outside and you need all they've got. My Z2 hasn't ever done this to me but I have had problems with an old Cadillac STS that I had when the battery started to go bad.
Also, remember that there is what is called a "surface charge" on the battery after it has been charged by the alternator. This will make the battery voltage look higher than it really is. If you took the 12.1-12.3V measurements right after you shut the engine off then you are likely looking at an "at rest voltage" of near 11.7-11.9V which is a "DEAD" battery.
Pick up a new battery and I'll bet the problem goes away.
Sorry if I rambled, I've been in this business with heavy trucks and off highway vehicles for many years and just put my work hat on for a few minutes here.
PM me if you need further help, I'm traveling this week but I'll respond when I can.
Cheers!
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