i have read articles stating that we tend to move our eyes unconsciously when accessing memories, as well as visualising and making up things. i’ll post a link when i get back to a computer. it is even suggested that these eye moments could reveal liars in police questionings. could the eye movements also be connected to HI, or visualising?
Asclepius, I’ve read that too. When you remember something, your eyes look, say, towards the upper right side, when you imagine something, you tend to look on the left, etc. And there was a psychologist who used this to suppress Vietnam veterans traumas by making their eyes look from right to left and left to right.
But when your eyes make lots of little and quick movements during your sleep, it’s called REM (rapid eye movements) because they are rapid eye movements. 
Anyways, I agree with you, scientists still don’t know why we do this: it was commonly believed that our eyes followed dream images, yet it’s no more accepted. And as during REM sleep, it seems that we access and consolidate memories, it is perhaps related to this.
It’s often observed with sick people cause normal people are generally not submitted to medical tests. 
But it seems it’s rather common and if I remember well, in one of the documents pointed above, tests were performed only on normal people and they were experiencing SOREM too.
When I was younger this used to happen when I concentrated too hard on seeing new things with my minds eye, by accident I was concentrating partly on my fleshy eyes and they were becoming stressed I guess. Like a muscle tensed for a while will begin to shake. They call it REM for odvious reasons. 