Off Balance

In the Batcave, Alfred can be seen polishing the giant penny to which Batman was tied during an encounter with Two-Face in Almost Got 'im (1992).

Batman states he was able to get through the vertigo trap by keeping his eyes closed and relying on his other senses. Vertigo affects the vestibular system which coordinates balance and is linked to the auditory system. Therefore closing one's eyes would not stop or even lessen the symptoms. In fact, closing your eyes could make the symptoms worse by further disorienting your balance.