What would cause your right eye to start blinking almost as if you are winking?

This is just a twitch that could be brought on by stress, tiredness or for no specific reason. It has to do with the nerve endings. This could be dangerous if it is associated with numbness, but I am not a doctor so please see one, it will ease your mind.

Another answer

I had a patient come in because her co-worker noticed that one of her eyes was blinking more than the other. She ended up having Bell's palsy. It would be worth calling your doctor, he or she will ask further questions to see if there is a concern or if it is as the previous person said, a twitch.

If twitching is a chronic problem and occurs as a "blinking" of the eye, it is called "blepharospasm". You can consult your optometrist about this problem and if required, they can refer you to an ophthalmologist to get injections of Botox which will temporarily control the twitching.