My 2002 Tundra V8 suffered from the same squeeking you have described. I thought it might have something to do with the A/C as it seemed to be loudest only when the A/C was on. I took it to the dealer and found out that I was wrong.

The mechanic replaced the belt tensioner (and the belt just because he had it apart I guess).
That was about 8,000 miles ago and I haven't had a squeek since. The best part was that I had 62,000 miles on the truck and they covered it under the warranty.
I hope this helps, even if your Tundra is out of warranty it should not be an expensive fix. Good luck!