changing 2000 honda civic domelight from incandescent bulb to LED panel- smoothing out PWM "dimming" with capacitor circuit
Maybe use fewer series LEDs (so that it's less sensitive to voltage) and just use an RC (split the series resistor). 470mA seems a bit high if you are using decent LEDs- usually the ratio between incandescent bulbs and LED is more in the 6:1 range, and low voltage tungsten bulbs tend to be less efficient. But maybe you want more light.. 

So if you use 2 LEDs in series and 13 pairs, each with 15mA, that's 200mA total. You need to drop about 8V with the motor running and maybe 5V with the motor off, so let's calculate for 7V, 3.5V across the string resistors, so about 220 ohms each and 3.5V across the series resistor so about 16 ohms. The RC thus sees about 8 ohms. If the RC is to be in the 100ms range you would need around 12,000uF, which isn't crazy big. You can recalculate for the larger capacitor required if you really want to go up to 470mA. But something in that range would likely work. The peak current (from the MOSFET or BJT driver in  your car) would be around 14V/16 ohms or 875mA which is probably acceptable since incandescent bulbs draw several times steady state current when cold. 







simulate this circuit &ndash; Schematic created using CircuitLab

Note: The driver is probably an open-drain or open-collector high side driver, so series diodes are not required and will add voltage drop. We're kind of guessing on the required time constant too. This is really the sort of thing where you are probably best to cut and try.