I have worked a bit with "smart" batteries. They have an IIC (SMB) interface and an integrated chip that will monitor the battery and take _everything_ into concideration. Like ageing. I admitt that was NiCd and not lead, but they did not work that well. It is a difficult task to figure out total capacity and remaining capacity even if you have the full history and knowledge about battery characteristics....
I also built a boombox/gethoblaster in the darkages with lead batteries, and in more resent years a boxcar for my son with motorcycle batteries. Experience from that is as expected that lead batteries are not well suited for deep discharge. You did not say what type your aux battery was, but lead is not such a good choise. Not just any car battery anyway.
So I guess best is to make sure the charging voltage is ok, and the charging current to make sure your car is charging properly and how low the battery charge was when starting up the motor.
Charging current can be measured over your fuse with a sensitive diff amp close to fuse.
If you build such a diff amp you can monitor battery voltage synchronized with current and calculate/estimate the resistance of the battery. If you are clever that should be possible to do in hw, but sw is easier. This will give some indication of battery charge, as resistance goes up with discharge. (and age etc). This require a lot of testing.
And/or do what ATX- powersupplies do. Monitor voltage and shutdown below threshold voltage after a timeout to protect the battery life length.