The amp's 12v trigger is only rated for 50mA. The fan in question wants 500mA, so that clearly won't do the job.

Given how many other wall-warts are floating around to drive all the doodads in the home theater, one more wall-wart isn't the end of the world, and the whole business goes to zero if I hit the great big power switch.

Presumably, that means I only need to get something like this and I'm done.

EDIT: Or they've got everything integrated and ready to go. That's probably the solution.