When I use a led and need to calculate a suited series resistor I just take the typical forward voltage from the spec and subtract it from the supply voltage.
I have NO spec for those LEDs, but I've made a plot of a few measured Vf(I) and now we can see that we can expect at 100mA current LEDs forward voltage around ~8.6Vf
Now, when we connect those LEDs to 12.3Vbat I have with 47R we can expect ~8.4Vf@83mA since:
(12.3Vbat-8.4Vf)/47R=0.0829~83mA
which leads to expected power loses in this 47R resistor:
0.083^2*47=0.3237~0.32W
while LEDs power ~0.7W
However, when we connect to running car 14Vbat by using this plot Vf(I) we can expect something like 113mA LEDs current (total in -> out regardless how those small 12 LEDs are internally connected):
(14Vcar-8.7Vf)/47R=0.1128~113mA
so we have power dissipation in 47R:
0.113^2*47R ~0.6W (teardown shows very small resistor which looks like 0.25W )
as well as LEDs power:
8.7Vf*0.113A=0.9831W ~1W