Nancy, I suspect that this newspaper notice is your Joseph M. BRIGGS. It's on PANB. The only difference is yours would be "J.M. BRIGGS" and T's and J's are often mis-transcribed.
"Date March 20 1852 County Saint John Place Saint John Newspaper New Brunswick Courier
Drowned at San Francisco, about 30th Jan., Capt. T.M. BRIGGS and George JACKSON of St. John city, N.B. The former had charge of a store ship and while endeavouring to get on board of her during a gale, the boat in which they were, upset."
I did the two cemeteries at Mispec and he's not there, so probably, as you suspect , he died away from home or didn't have a stone. Also I can't see any Capt. T.M. BRIGGS mentioned in Saint John. So I imagine he was buried in San Francisco. None of the BRIGGS sons are buried in Mispec. Hope this helps, Suzanne Carter