What does it mean when someone gives you little or no eye contact ?

Shy: I would say the most likely thing is that the person may simply be shy. We have all seen young children who hide behind their mothers legs and will not look at you. Certaninly other types of behavior can lead to this also. If a patient has an eye disease of certain type, such as inflammatory eye disease, they may be light sensitive and not look at you simply due to lighting situations.