It could be the HID. If they (the ballast) don't have a clean earth straight back to the battery negative they can cause all sorts strange electrical issues. Disconnect the ballast and see if the problem with the tail light is cured.

However, as you say its OK on a cold start up, it is much more likely the LED unit itself is at fault. When cool it works, and as it heats up it breaks down.

Most people assume LEDs don't produce heat like normal filament bulbs, but they do, it's just that it is not radiant heat so it's not noticeable. LEDs heat up to fairly high temperatures internally - it's called junction temperature, where the positive and negative parts of the semiconductor meet (the junction).



Juntion temperature is the same reason computer processors, chips etc. need a heat sink and cooling fan and often fail through heat shock. Just take a look at the size of the heatsink/fans on the back of a BMW GS with an LED headlight to get an idea of the heat produced by bigger LEDs!

Try connecting up a standard bulb/tail light and see if the problem goes away, or try another LED unit. LEDs that have failed at the junction cannot be repaired.

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