Trying to figure out who the mother of Elisha Beckwith, b. 1761 is.

Elisha (1761) m. Grace Leach.

Elisha's father was also Elisha, b. 1735, son of John Beckwith and possibly Hannah Brooks.

I have found a suggestion that Elisha Beckwith (1735) was m. to 'a daughter of Nehemiah Smith', and I'd like to prove or disprove this.

I did find a reference in "A genealogical history of the descendants of the Rev. Nehemiah Smith of New London Cty., Conn.", by Henry Allen Smith, to a Lydia Smith, (Samuel/Nehemiah/Nehemiah) who married an Elisha Beckwith, but there is no information on who his parents were. This Lydia Smith and Elisha Beckwith did have a son, Elisha, but his marriage as listed in this book is not to Grace Leach -- though it could reference an earlier marriage to Sally Miller.

Can anyone point me in the right direction?