As per Captain John Wenz
"If the switch is in the “BOTH” position and one battery is nearly at a full charge and one is flat, the alternator will “read” the higher of the two, and the flat battery will never be charged."
This above statement by Captain John Wenz is definitely incorrect!!..........Less any differences in internal/ext resistances and possible temperature differences between each battery, for all intents and purposes, when switched into "both", both batteries are now paralleled together, as such, they are now "hard wired" as one BIG battery (2X the capacity if they're same capacity).
It's therefor electrically impossible for the "alternator to “read” the higher of the two" since, as stated above, beings now they're hard wired in parallel via this new buss bar, there can't be "higher of the two" per-se because there is only ONE battery now. A bigger one but, none the less, just one!! Making his statement quite false!!
When switched to both, at the second the switch/wiring connects both batteries together in parallel, they are forced to equalize their charge, this happens in milliseconds if wiring and internal resistance is small'ish.
e.g., if one battery is higher in charge (not capacity) then the other, the higher of the two will always dump(dis-charge) and "equalizes" its charge with the lower of the two.
If and when the engine starts up, all's the alternator knows is there is a battery out there and it starts to charge it.....One, two or twelve, if they are in parallel, it's either become a big, or it's a medium or a small battery depent on the switchs' line-up, it knows no better, it's always just one battery to the alternator and it charges it as best it can depending on it's new capacity.