Well, they use a pellet in those headlights, right? I bet the chemistry in those is biased towards 405 producing the brightest color white because my disk doesn't respond well at all to 405nm. I tried 980mw of 405nm and it is far lower output than my 1.9 watt 445nm blue and the color spectrum isn't nearly as white, more yellow-white.
I put both beams on the disk and 445nm produces about 20 times more brilliant white light than 405nm which when compared side by side, the 405nm "white" product looks more violet-white. It must be a chemistry bias toward 445nm on this particular product.
Edit:
More testing done: The white light coming off of the remote disk doesn't want to collimate like a laser beam, I guess that should be no surprise, given the large diameter. If I had a tiny bead made out of this material and passed the 445nm beam through it, I think it would collimate into a tight white light beam very nicely, but never as tight as a regular laser beam.