"Maine, Nathan Hale Cemetery Collection, ca. 1780-1980," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QVJ5-QQC6 : 1 March 2021), John Burnham, 1888; citing South Newcastle, Lincoln, Maine, United States, Malcolm Cemetery, Maine State Library, Augusta; FHL microfilm 1,315,041.
I believe this John Burnham [ Burnham-630] is not the child of Zaccheus and Elizabeth. I believe that Harris and William are the sons of John Burnham born 1779. -1840, brother of Zaccheus Burnham. I shall someday hope to the have the time to help prove this with sources. In the meantime this comment will have to do. :}