Jaw winking phenomena is caused by abnormal wiring of the nerves from the brain, in which there is drooping of the upper eyelid in the affected eye and when the jaw moves while chewing anything, the drooping eyelid moves up and down with chewing movement.
This is present since birth and nothing needs to be done. It does not affect the eye sight ever and at most it could be a cosmetic embarrassment. Imagine wrong wiring in which fan runs instead of light turning on when light switch is pressed and vice versa. Similarly, the nerve to the eyelid goes to muscle of mastication and vice versa.
If you do want surgery for it then it is possible to cut the nerve which moves the eyelid up and down and then correct the subsequent drooping of the eye lid by surgery, however I would not advise surgery as it may not be 100% successful and there are chances of complications.