Is it just a noun, or is there a more precise name? It seems like an object of the preposition, but I'm not sure.
closed as off-topic by tchrist♦, Chenmunka, Centaurus, Edwin Ashworth, ScotM Mar 20 '15 at 0:52
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Of course it's a noun. A noun, as the song goes, is a person, place, or thing, and touch is certainly a thing.
In this sentence, it is the object of the preposition of, but the the object of preposition is always a noun-phrase of one sort or another (e.g. a noun, a pronoun, something like that).