In the books, it is made clear the helmet did not cover his eyes, as when Aragorn looked directly into his eyes, the Mouth of Sauron was really afraid.
So this is no idea of Tolkien's, just another PJ invention. The idea is that he could see with the help of dark magic, and so didn't need normal sight anymore. I think it makes pretty little sense, as the Mouth was after all only a Black Numenorean.
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“The invisible and the non-existent look very much alike.”
Delos B. McKown
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