Oh boy. No. Slowing your breathing is not going to protect against the effects of electrically stimulating the vagus nerve. Whether or not the TENS approach to vagus nerve simulation is effective or not, please don't believe this will somehow help.

I think the advice was to forgo TENS in favor of breathing, not to mitigate adverse effects of TENS with breathing.

This is correct. Apologies for the ambiguity in my comment.

Ah!! Then you have my apologies for my misinterpretation too :)

Thanks for clarifying, it seems I did misunderstand. Too late to edit unfortunately.

Would you have a source for this?