Hmmmm…
My guess is that it means that you either "never look the other person in the eye", or that you "keep your eye on them in a dead stare". I suppose that folks typically do an unconscious dance with the other person's eyes while conversing-alternating between contacting and then looking away and then looking back. So its not either of the two extremes of either never eye contacting nor constant eye contact. But that's just a guess.