I came out to find the puddle light dangling from the passenger side mirror about 6 months ago. It seems that on the light there is a little clip built in that holds the light in place. Magically it broke and the light fell out. (Don't know how; I'd never tried to take the light out before - seriously.)
I put it back in place with a piece of clear packing tape across the bottom of the mirror. When I had to bring my AV in for the clunk in the steering wheel, I told them about the puddle light. They replaced the whole mirror under warranty, which I didn't expect.
I would check with your dealer first. If they won't help you out, I'd go to a junk yard and get one there. I image that they are the same little puddle light that is on a Yukon or Tahoe mirror.