Here I did a quick design with window comparators using LED's for reference voltages and indicators, which are entirely optional.
All you need is the top comparator (quad type) to indicate low voltage , the trigger for starter ON. and the bottom for ALTERNATOR ON.( engine running)
The string of 4 White LEDs like a 12V zener for detecting battery voltage as it cycles from starter ON below 11.5V and Alternator ON > 13.5V ( normally 14.2V)
play here
Of course you may use ADC and do this in a uC if you prefer and amplify the diode string current to 3V and even connect an analog Volt meter to show actual Vbat. with a more sensitive range than 0~15. The lower the current you put thru the LED's , Series R, the more accurate the voltage sense or quality of the Zener like characteristics. .i.e 0.1 ~ 2mA will be approx 2.8 to 2.95V ( work better than most Zeners at this current and voltage level) But I raised the current to make the simulator bright with 82R.
The 1 Ohm should be a polyfuse., the 5V Zener can be an LDO and the comparators can run off 5V and be open collector type with Red LEDs giving 5-2V= 3V logic level out or Op Amps as I selected here.
This is just a quick and dirty design..... TONY
The theory of operation is solely based on Vbat. to indicate 3 states, Starter ON, Engine Off/idle, Running.