Let's consider the similar determiner "none of", that we would use with more than two items*:
However, this mirror will give us none of knowledge, truth or wisdom.
That seems pretty valid, no?
Let's also consider if the two qualities had been mentioned first, and use neither in its determiner sense:
We seek knowledge and truth. However, this mirror will give us neither prize.
So, it seems by analogy that the first sentence is indeed using neither in its determiner sense. It's amusing that the meaning is that the mirror will give neither knowledge nor truth - the same meaning as the second sentence.
I would advise against the construction though, if only for the simple reason that it might lead some readers to ask questions like this. Therefore I'd favour the second sentence in its place.
*Opinions differ as to whether neither is allowed with more than two items, but that's not really relevant here.