Someone can correct me if I'm wrong, but my understanding is the 12v battery is charged from the main battery using the DC-DC convertor, which is only active when a contactor is closed that happens when you key the bike on. It shouldn't really take too long to top it back up. I'm not sure how easy it is but you could always just disconnect the 12v battery if you can do without the always on cell connection.
Instead of guessing that the 12V battery charges when the Zero DSR/X is charging, I just went out to check with a digital voltmeter.
My Zero DSR/X main battery is already fully charged, as I plan on going for a ride in the morning. My 12-volt battery is already charged up fully, but I did the testing anyway.
12-Volt battery, key off, NOT charging=13.08 volts
12-Volt Battery, keyed on, not charging bike=13.23 volts.
12-volt battery, charging for just a few seconds, keyed off 13.33 volts.
And I double checked all that because it was all close. All tested the same.
While there would be a larger difference if I were not already at 100% SOC, above is enough to convince me the 12-volt battery is charging when the bike is charging as well as when keyed on, charging or not.
IOW, the only time the bike is NOT charging the 12-volt battery is when the bike is off and not keyed or charging.
But . . . .
I have no way to test what happens in the storage mode at this time, but I assume then the 12-volt battery gets charged up only when the main battery is charging, which means the main battery has to get quite low before the 12-volt battery will charge. This means it is possible that that charge will not be long enough to recharge the 12-volt battery, because it may only need to charge the main battery for a few minutes. IOW, in the storage mode, the charger is mainly off.
IOW, it is possible for the 12-volt battery to become discharged in the storage mode, but not when normally charging.
To get a full charge on the 12-volt battery, it will probably take a few hours if it is already greatly discharged. That will not happen in the storage mode.
-Don- Auburn, CA