or does there need to be some juice in the 12V to begin the charging process?
There needs to be some juice in the 12V to begin the charging process.
Before you can do anything with the big battery, you need to close the contactors inside it, and for that you need a little energy from the 12V battery. A lot of computers wake up at this point, so they need some 12V energy too. Ten seconds after plugging in an EVSE or a DC charger, the car's DC-DC can take over the 12V duties, including recharging the 12V battery.
It's worth remembering that allowing the standard lead acid 12V battery to go totally flat, even for a day or so, pretty much ruins it. If the time it spends being totally flat is short, it might recover enough to work for a while, but it will be wounded, i.e. it will have suffered some degradation, in other words, a loss of capacity.
If you had to leave an EV at the airport regularly and can't rely on AC power for trickle charging, or a solar panel, you could replace the lead acid 12V with an expensive LFP model, which has a battery management system that can save it from such degradation. Then a portable recharger in a fireproof bag could get the car going again after many times when the 12V ran flat, and the LFP battery should survive this punishment.
Of course the best solution is for the car itself to automatically charge the 12V battery as needed, at least until the main battery reaches a low SoC limit. Out If Spec Reviews did a video on an EV abandoned for something like 10 years. The 12V battery was toast, but the traction battery was still at 30%, having charged the 12V battery as needed until the traction battery reached 30% SoC itself. There are a few posts on this forum about it, which is how I heard about it. But I suspect that MGs don't all do this. My ZS Mark 1 in particular never seems to charge the 12V battery. Maybe I never leave it undriven for long enough.