I have a document contributed by one John Wood, 145 Glenbrook Cresc, Pointe Claire, Quebec H9R 3X9. On page 32 in the footnote 2b there is a sentence which reads: "Anon. description in the FHC of a plaque erected by the DAR on Staten Island. General Joshua, Colonel Jacob, (another) Captain John, (soldier) Cornelius, and (sailor) Paul Mersereau were brothers who "served in the revolutionary war".
I hope this might aid in your attempts to identify your Jacob's role in military service. As some Mersereau males elected to support the loyalist cause, one cannnot tell from the above whether they all served the patriot cause or not. One would think that if it were erected by the DAR, they would all be patriots.
I am descended from one Ellen Maria Mersereau,(b.1823) daughter of Daniel Mersereau (b.1803 and Ellen Maria Lozier (b.1799) all of Staten Island and I've still got some sorting out to do to identify all of them to the emigrant ancestor. Good luck to you in your quest.