What charges the 12V battery? Just running the ICE?
Any time the green "ready" light is on for the car to drive the 12V battery is being charged.
While the car is plugged in to the EVSE, it is also charged, though there seems to be some question as to if it's charging all the time or not. I wouldn't be surprised if it's only charging the 12V at the same time it's doing charging of the HV battery, but that occurs more than once on mine. Like if my car is fully charged but then I go out the next morning and open a door it seems to top off the charge. And Go times also and any other time you hear the fan running. All of those would be times that the 12V would have to be charging while plugged in.