This description of the Horizontal Gaze Nystagmus test posted by California DUI Lawyer.

Opto-kinetic nystagmus can occur when a person focuses on several objects at one time or objects that are moving away. An example of this is when a person looks at objects out the window of a fast moving train. This is the reason that officers are instructed that the quiet background to perform this test should be away from the view of passing motorists and bright or rotating lights. 

Nystagmus is the involuntary jerking of the eyes. The first clue is known as Smooth Pursuit . The officer is looking for the suspect's inability to pursue a moving stimulus smoothly while focusing the stimulus being moved horizontally, from side to side. If the suspect moves his head to the side at any time, the test is invalid and should not be scored.