How Big for 12V Aux Battery?

Are you using a 12v step down converter from your main traction pack? You would just need to know the idle current draw of components with the car off (such as keyless entry, alarm, radio) and then calculate how long you want the car to have power on standby.

Once the 12v step down converter is active, your 12v battery will be recharged. However, if you are not using one, you will need to know the draw of your aux components like a water pump, fan, etc.

I wonder if there is enough significant benifit to using a lithium battery as apposed to a regular AGM car battery... Probably not going to draw that much current.

Anything will work. Find the smallest, cheapest AGM battery and go for it. Mine was smaller than a Rubik's Cube. "Jumping" the car involves, like, touching any good 12V battery to the DC/DC terminals to wake it up. You could throw one in the glovebox.

Specifically, the battery doesn't power anything—it just starts up the computers. When the DC/DC converter is on, the battery is just another load, like a headlight.

The thing you will have to worry about is what happens when the DC-DC dies and you're on the highway at night, etc...? You'll need to have enough juice to, like, pull over and maybe throw the hazards on.

Lithium doesn't seem worth it because they're finicky about charging, and in an EV the 12V battery will pretty much just get a constant voltage of ~14.2 with no smarts for charging. With the size of the battery you need, you're talking about saving a pound or two, I expect...