LED's require much less voltage and current than a normal bulb. If the codes don't show it is a problem and the light is off when using a incandescent bulb then the ABS should be fine. Try this put a meter in series with a regular bulb and measure the current draw, and again with the LED. It does not take much current to light up an LED, a level that you'd never notice with a standard bulb.

to fix it ... add a resistor in series with the LED to try to get rid of the phantom glow, which will also make it dimmer when on as well.

A few parts from digikey could build you a circuit to only turn on the LED when it is really on. a comparator a few resistors etc.