Ok - the pic below is the circuit... (Redrawn, but still with thanks to R. Paisley.)
Note that no protection circuitry (diodes) is shown. This is just the basic circuit...
R2 is the bulb and R1 the low value (aka power) resistor (which may need to be bigger than 1/2W for some values & bulbs).
The tested bulb(s) R2 vary from approx 20 Ohm (7W taillight) to 3 Ohm (2x 23W stop) or 1.5 Ohm (4x stop).
The voltage at the power-resistor/bulb junction (R1-R2 & "-" input) has to match the the voltage at the R3-R4 junction (+ input) for the comparator to be at its switching point.
Hence adjust R4 so the LED just turns off with the bulbs as normal (engine off is fine - no voltage regulation is involved hence circuit remains "balanced").
The biggest voltage drop across the bulb's power resistor R1 is when all bulbs are operating. (ie, V=IR so V is max when current I is max, ie, the most bulbs.)
Whilst R1's voltage drop exceeds that of R3, the inverting or "-" input voltage is LOWER than the non-inverting or "+" input, and hence the comparator (output) is off (ie, floating).
If a bulb blows, the current should be lower (or nil) thru R1 so that - subtracted from the +12V rail - means that the "-" voltage rises and should be above the "+" input, hence the comparator turns on - ie, the output connects to 0V/GND and can sink 16mA, hence R-LED RL should be ~12V/0.017A = 706 Ohms => 820 Ohms (1/2W though 1/4W may be ok).
IE - the comparator turns on a LED connected through an 820 Ohm (1/2W) resistor to +12V. The 820R limits the (LED) current to under 16mA to protect the LM339 output.
BTW - I chose 10k for the R4 trimpot as it's a common size; not too much current but enough to generally swamp car noise.
I also chose the voltage drop across R1 & R3 to be 0.5V, though a mere 0.05V should also work - but I'm unsure of comparator behavior with near +V inputs - it should IMO be ok; but most comparators compare voltages closer to 0V/GND.
One problem with a regulated supply is that the Comparator and R3 & R4 have constant voltage but the bulb input does not since it is powered from the vehicle's +12V and hence can vary from (say) 12V to 14.5V, or 20%.
That shouldn't be a problem for single & dual bulbs, but may be a problem for 4 bulbs depending on trimpot sensitivity. (Sensing 4 bulbs means sensing a 25% change (1 of 4), but the signal varies 20%, hence only a
5% adjustment tolerance".
If you include cranking - hence 9V to 14.5V or 45%. So sensing 2 bulbs (50%) is possible...)
The unregulated circuit doesn't have that issue - as the vehicle voltage varies, so do the "reference" points (ie, BOTH the + & - input voltages react similarly to voltage changes so it shouldn't false-switch).
I'd forgotten that Op-Amps and Comparators handle up to 35V supplies and hence can be used in "raw" +12V car environments (excluding spike protection (zenor & resistor, & run LED/load from raw +12V.) Good-bye evil voltage regulators and voltage restrictions.