I'm not a doctor either, but from what I've found, you are correct about it being the vagus nerve. It's currently being called Arnold's nerve cough reflex. Here's a link to a 2014 article about it: https://pmc.ncbi.nlm.nih.gov/articles/PMC4222929/
When I first got a PS4 and tried to connect my headset to it I was told of was unsupported. After doing some digging I found that the only supported bluetooth headsets were specifically the ones that were branded as PlayStation. This wasn't the case with the PS3, it was just a decision Sony made in order to sell their overpriced headsets.
I'm not a doctor either, but from what I've found, you are correct about it being the vagus nerve. It's currently being called Arnold's nerve cough reflex. Here's a link to a 2014 article about it: https://pmc.ncbi.nlm.nih.gov/articles/PMC4222929/