"John Elliot, d. 1807" is listed on one of the multi-name stones in the Peirce family plot (Section 77, Lot 24) but there is no burial record for him listed in the database.
Box 38, Folder 4: Elliot, Dr. John: Funeral invitation, obituary. (The obituary from the Dayton Repertory states that he died Feb. 26, 1809, but H. G. Phillips' letter clearly states that he died "this morning" on Feb. 27.)