Hi Tige3rs,
Your boyfriend’s cousin may keep staring at you because he has developed a crush on you.
He may not have a girlfriend at the moment to occupy his time and thoughts.
Without that kind of distraction, he may find himself unable to stop staring at you on a number of occasions whenever he is around you.
If this is a light crush, it may fizzle out in time if you avoid being around him for the next four to six weeks.
Try doing that for now and see if you notice a change in his behavior after those weeks have expended.