That's what I was about to say. SPs are great at randomness. And Letterman tends to focus on one word or phrase he decides is hilarious to him and he then repeats it over and over again throughout the show, then the next day it's something else. It's very easy to tell what bits are done by his writers and what is just his ad-libbing. He most likely has some N writers but he is personally SP. Punching the camera, throwing pencils, dropping fruit off of high buildings, covering himself in alka-seltzer and dipping himself in water, same thing with cereal and milk, random vocal instructions fed to the Deli guy, spontaneous and impulsive humor all the way. There's ample evidence to support his being an introvert, and he definitely strikes me as someone who tends to lean towards logical reasoning in his interviews/arguments and less to emotional value-type discussion.
So once again, I say ISTP.
These days, I think Jim Rome fills the spot as my favorite talk show host. His radio show that is, not his tv show. And his humor is very much like Letterman's early stuff. I think Rome is an ISTP also.