Canine rapid eye movement?

We have it because that is when we dream.

Rapid eye movement (REM) sleep-- A phase of sleep during which the person's eyes move rapidly beneath the lids. It accounts for 20-25% of sleep time. Dreaming occurs during REM sleep.

sleeping

Rapid eye movement (REM) occurs when you are asleep and when you are dreaming your eyes move to see the images in your dream which your brain is thinking of. Usually 25% of sleeping is dreaming and...

Yes it is....ive actually witnessed this myself on many occassions.....some people have involuntary eye twitches while they sleep.