This sentence is about wearing glasses rather than contact lenses. "Wire-rim" describes the design that is a thin metal frame around the lenses of the glasses. Pull up an image of John Lennon wearing his classic "wire-rim" glasses. The use of the verb "perched" just means that the glasses were resting or positioned on his nose. We also frequently use the verb "perched" to describe birds resting on a branch of a tree. And it sounds like the character described in this sentence was very recently wearing his contacts since contacts can often make our eyes red and uncomfortable. Poor guy!
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