How do you know that he still has eyes while he is sleeping? Generally, eyes are hidden behind some kind of lid to prevent light from waking the sleeper up. That's what those curved lines represent in the comic. Those ain't eyes, they are shorthand for "the eyes are not visible anymore". Whether that's because MitD has eyelids or because the proteans autonomic system has disposed of the eyes to make sleep easier, we cannot tell. All we can tell is "the eyes aren't visible anymore".
Heck, it's ridiculous to start with that, whatever MitD is, he'd sleep with his face aligned with the rather high window of his box. Almost every creature I can picture would lay down its head such that it wouldn't be lined up, so the very fact we can see the eye lines at all is just the tell that he is asleep*, just as the "he is saying 'zzzzzz'" is a tell he is lightly snoring, despite that probably only being the sounds a human makes and would not apply to any other species.
Grey Wolf
*And I don't mean just the head. Like, I'd expect most creatures to lay down to sleep. Not many species sleep standing up.