What is the cause of quick, random pain at the back of the right eye ?

Dry eye: Sharp, stabbing pains in the eye are often a sign of dryness. I recommend using otc artificial tears up to four times per day to help with these symptoms. If you are experiencing a different symptom, longer than a few seconds or associated with blurred vision, you should see your eye md.

Dr Ali agreed

Likely dry eye: Dry eye is the most common cause of sharp pain in and around an eye of short duration. Many other issues can cause similiar symptoms though. Try using frequent artificial tears and see if the issues improves. If it persists or worsens, go see an eye doctor.