Addendum January 2011:
TA-DA!!! We may have a winner here. With all the LED devices appearing on the market lately this had to happen sometime. This is an LED "bulb" configured as a direct replacement for the standard dual filament bulb. With 60 Bright White LEDs it radiates light in all directions, similar to the incandescent bulb, and "should" be somewhat brighter (maybe).

There is also an eBay listing for a Red 36 light LED bulb to fit the same application. Being red light output this might display similar light intensity after passing through the red filter tail light lens.

These parts are listed for $1-USD plus shipping. The eBay seller is eleseed. The same seller has hundreds of listings for other LED devices.


Addendum August 2012:
On 8/18/2012, Andy Badeker wrote:
"I have some great Hong Kong LED bulbs that are a perfect replacement for the brake/taillight and turn signals -- until you subject them to full service amps, apparently. While testing my rewiring job with a battery charger, per your suggestion, all was well. Once I hooked up the battery, nothing. After a brief panic and a sniff test under the dash, I returned the boring old incandescents to service, and all is well. But those LEDs sure were pretty while they lasted ... Nice and bright. Large white one is brake/tail bulb (but illuminates red). Small yellow one is turn signal (illuminates white)". -- Andy

Well, the answer to this puzzler is that Light Emitting Diodes are above all else, diodes, which means they only pass current in one direction. LED's, like alternators, are nearly always negative ground devices. Andy had the battery charger connected negative to ground while doing his wiring, so the LEDs worked. Then he installed the battery with positive ground, and the LEDs didn't work. His solution is to change the car's electrical system to negative earth, which is pretty easy to do (whenever he will get around to it).