How are they proof ?
In any case, Sharingan isn't Byakugan. So unless it's said so, their functions aren't the same. But really, by that logic, a dojutsu would shut off every time a user blinks and they'd need to reactivate it.
Not at all. The eyelids would prevent chakra from entering the Hyuga's eyes [visual genjutsu works by putting chakra into the opponent's eyes, sound genjutsu works by doing it through the ears]. Meanwhile, the Byakugan would still allow them to see where their opponent is and fight normally.