There are lots of different types of nystagmus, which are classified by things like how the eyes move (pendular, upbeat, downbeat, jerk, etc) and if it is constant or only occurs under certain conditions (such as head position, response to certain stimuli, etc).
Different forms of nystagmus caused by a lot of different things. Some causes include: neurological issues, vestibular issues, structural problem with the eyes, substance induced (medications or toxins), injury-induced, various other syndromes, etc.
My DS has autism and also has albinism. Albinism is a pigment disorder that causes structural defects of the eyes and results in vision impairment. Nystagmus is usually (but not always) a part of albinism. My son is lucky in that his vision impairments are relatively mild. He has very mild intermittent nystagmus. Most of the time it isn't there. But if DS is very tired or if the lighting is a certain way, we can see his eyes "dance" (pendular nystagmus).
I would suggest you have your son examined by a pediatric ophthalmologist as a first step.