Ok, wiseasses. No luck on this one, took some figuring out that it would be made easily accessible and how to unscrew the vent.
But here's the big question now - it does not seem to be the tube. Does a unit like this make use of a starter and ballast, and where are they located. I'm getting the sneaky feeling I'm going to have to remove the entire unit from the ceiling. And if I do that I'm going to look at replacing the 22W(!) CFL with a LED.