The darting movement back and forth of your son's eye is called nystagmus
. If this nystagmus started in the past few weeks, then you need to have it evaluated by a neurologist
as it can be from neural problem. If this nystagmus has been there ever since he was a child, then it is going to stay and he will be able to stop it if he focuses on something at near.
Hope this helps
Dr. Jay Patel