I think the 12V battery charges whenever the main contactor is closed. How familiar are you with Zeros? When you key on, you should hear small relays closing as they bike performs diagnostics and, if safe, the main contactor will close with a louder click. How good a mechanic are you? You might want to follow the directions in the manual to remove the seat and battery cover to check the voltage. If the main contactor is closing, you shouldn't need to charge the 12V battery yourself. If the contactor isn't closing, and the battery voltage is close to 10V, and you have a 12V Li-Ion battery charger or equivalent, and an appreciation for everything that can go wrong charging batteries, you might want to TAKE THE 12V BATTERY OUT OF THE BIKE and charge it to at least 12V. The battery will have to be charged if you want to continue diagnostics while waiting for the bike to dry out if the initial problem was an moisture induced isolation fault. If this is getting overwhelming, you'll need to make arrangements to get the bike to the dealer. Warning, it might sit there for a while.
I don't know everything that will drain the 12V battery, but the cellular connection certainly does. There is a battery heater, and it's unclear to me if this operates in cold temperature with the bike off.