Sometimes when I see a light that is, well, out of tune 
, I see these alternating bands of dark undulating along the tube.
What is the mechanism creating these waves of light and dark?
Fluorescent tubes emit most of their visible light from the phosphor coating on the inside of the glass; this is excited by ultraviolet light emitted by energised plasma inside the tube; if there was no phosphor coating (and if it was safe to look at them), the inside of the tube would look a bit like those Plasma Lamps and undulates/pulsates for similar reasons. You can’t see it as clearly in a fluorescent tube because you’re just seeing the effect it has upon the phosphor coating.
The constricted shape of the tube itself, as well as the composition of the plasma, also defines and limits the range and type of undulation you’re seeing.