carbon resistors fail when stressed
It may also be a deliberate limitation of the lifetime of this LED lamp by the manufacturer
(it was quite cheap one) through the accelerated destruction of this resistor and, as a result, possibly also LEDs - car users are used to the fact that the light bulbs burn out
I've connected those LEDs now again to 12.3Vcc battery, but by using 100R 0.25W resistor and we have slightly higher 8.13Vf@41mA on those LEDs while 4.1Vr voltage drop over this resistor
However, no supprise because of when I've estimated before this test LEDs current for custom battery 3s Li-on 4.2Vmax charged up to 3.9V to extend lifespan of its cells, we get nice LEDs cuttoff even when voltage on single battery cell will drop to 2.6V:
(3*2.6-7.77)/100=0.1mA
while when fully charged:
(3*3.9-8)/100=0.036A~40mA
When used in a car where I have around 14V when running:
(14.0-8)/100= 60mA
so estimated power dissipation in 100R resistor will be: 0.06^2*100~0.4W
which looks much better then oryginal design.
LEDs will output then around: 8*0.060~0.5W
which is not so bad, while even at 40mA light is very bright from this thing
NOTE: While we know expected forvard voltage of those LEDs there is poblem in using LM317, since as I know it need input voltage +4.25V higher than regulated output, so it doesn't look good now even in the case of 12Vcc battery (especially my custom 3*3.9Vmax=11.7Vmax) , while maybe it could be fine in a running car at 14Vcc:
14Vcc-8V=6V