I have a 2005 RR HSE and with the lights on,
the right HID lamp will flash to an extra brightness then come back to its normal output, the flashing causes the left lamp to dim, this is when driving with the lights on for a a while.
NOTE the DTRL are engaged so the lamps are running all the time, , might it be a relay?

 

The igniter is dying on the flashing headlight. It is switching back and forth from startup to run mode. (startup juices the bulb with extra voltage/current when it is cold, this leaves less current for the other igniter). Cheapo Chinese HID Igniters on ebay work fine for replacements.

 

Google Image Result for http://www.philipshidkits.com/product_images/b/314/1226943564__61243_thumb.jpg

might this work and where is this part on the headlamp

 

http://cgi.ebay.com/ebaymotors/Slim-...#ht_6283wt_992

These are the cheapo ones im talking about... I have used them to replace BMW/Mercedes igniters, they work like OEM at a fraction of the price. All the ones I replaced are still working years later.