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battery types

A normal car battery (lead-acid) isn't designed to be discharged very much. It's designed for very-short-term surge applications, not for running things overnight.

A deep-cycle battery (AKA marine battery) is designed to handle a load for hours at a time.

cutoff percentage

If you don't want to deep-cycle a normal lead-acid battery, then you should cutoff the battery at 80-90% charge. That website says this equates to 12.4 volts.