Hi Anne B.,
I suspect there are two different Nathan's attached as children because Walter Goodwin Davis identified their son Nathan as the immigrant who was of Amesbury.
Donald Lines Jacobus identified their son Nathan as the immigrant who was of Fairfield.
Thus, we have two real persons, Nathan, each attributed by great genealogists to have been the son of John and Judith ___ Gould.
Walter Goodwin Davis, ''The Ancestry of Dudley Wildes, 1759-1820, of Topsfield, Massachusetts.'' (Portland, Me. : Anthoensen Press, 1959). 101-106 (VIII. Gould); digital images, [https://hdl.handle.net/2027/wu.89061707337?urlappend=%3Bseq=119
''Hathi Trust'']; children of II John Gould, p. 102-103.
Donald Lines Jacobus, ''The ancestry of Lorenzo Ackley & his wife Emma Arabella Bosworth'' (Woodstock, Vt. The Elm Tree Press, 1960), 194-195 (Nathan Gould: Fairfield, Connecticut); digital images, [https://hdl.handle.net/2027/wu.89062958764?urlappend=%3Bseq=262