A bit of a follow up. I've tested my daughter and she definitely shows a relationship to my mystery cousin. I also uploaded my DNA results and the "cousin" uploaded his as well to Gedmatch and we show a good match there as well. So there's definitely some kind of connection. We still don't know how it came about.
I've considered the possibilities and concluded that this person's father's mother's mother's line is probably where the connection is and as it happens it goes up my female line as well. So, I'm wondering if the father and I did mtDNA tests if that would narrow the search. What I'm asking is does mtDNA identify a recent family connection. I know it's used to identify ancient population groups but would it help me with this situation?