Here's what I was able to locate using Google and "general parsons" and NC to search--
This is the one that says General Parsons was a brigade commander of the NC militia in 1776.
This one says he knew General Parsons later in the war.
I did a search in American Archives looking for Parsons but found nothing that didn't look like S.H. Parsons of CT. The NC Provincial Congress records might yield something. There is also a DAR list for NC that I don't have that may turn some leads.
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