Actually, it’s not just floating eyeballs. It’s disassociated body parts in general. Eyes are possibly the most common offenders — “her eyes darted around the room,” “his eyes fell to the floor,” and so on — but just about any part of the external anatomy can suddenly start wandering around and acting on its own. (When this happens in the romance and erotica genres, the results can be . . . disconcerting, to say the least.) At least in my opinion, if the word “eyes” can be replaced by “gaze” without changing the meaning of the sentence, then it damned well should be.
Likewise, if the whole sentence could just as easily be phrased, “he/she looked at whatever-it-was”, then for heaven’s sake, write it that way.
Disassociated body parts turn up in all sorts of writing, but the problem is most acute, and most dangerous, in the science fiction and fantasy genres. Why? Because those are the genres in which metaphor becomes reified, and in which — for example — detachable and/or self-propelled eyeballs are not outside the realm of possibility.
(I can think of at least three fantasy/science fiction examples right off the top of my head, and I’ll bet you can, too.)