help with voltage/frequency fluctuations

I am trying to run a lcd display in the car. the backlight of the screen is obviously being affected by the alternator as as the RPMs change the rolling of the backlight changes. What would be the simplest way to smooth out the power coming in. The screen runs on 12v (safe 10-14v) and at around 600mA. I was thinking that a simple capacitor inline to the power in on the screen, would act as a filter. Its been many years since Electronics class so I'm not 100% on that. If a cap or anything else, what size/value should I use?

Is the backlight incandescent, or florescent?

I don't think you can put in a capacitor big enough, unless maybe it is one of the 1 Farad types much beloved by car audio nuts. C×ΔV = I×t. The minimum alternator ripple freq is ~200 Hz, so t=5ms. I=0.6A. An allowable ΔV might be 100mV, so C=0.6×0.005/0.1 = 0.03F, or 30,000uF.

I would use an Low-Dropout IC Regulator to reduce the voltage to a well-regulated 10V, and run the display on that.