I want to use "listening" such that it modifies "the vogue", not "the people."
Which sentence achieves that? Or neither?
The vogue of people listening to music on tapes is not completely gone.
The vogue of people's listening to music on tapes is not completely gone.
So "the vogue" is the act of listening music on tape.
I also don't know what "listening" would be grammatically called in each sentence: "gerund" or "participle"?.