That's a good question. The 12V battery isn't as large as a ICE car battery and of course you don't want to run it down. I think the car has to stay "on" for it to use the high voltage battery to recharge the 12V battery. I'm not sure how to ensure the HVB is recharging the 12V.
One other thing to consider is that when the car is "on", the screen may also be lit and bright. On that note, I have a dark sheet that I throw over the roof of my car to keep interior lights from possibly disturbing others at star parties.
Consider buying a Li-ion battery, that would be lighter than a lead-acid battery, to power the scope. I wouldn't risk killing your 12V battery, unless you have high confidence that it's being charged by the HVB.