Thomas Baker's father's information is uncertain.
I saw that John Annable (Annable-4) had a daughter, Mary Annable (Annable-334) who married a Thomas Baker who died in Shrewsbury. I created a profile for Thomas' father with rough estimated dates. (Baker-56435) Still seeking birth and death information for Thomas' father and to ascertain Thomas' paternal grandparents.
As noted in my response to a comment, there are two individuals named Thomas Baker, both who married a Mary, seemingly both with the purported same birth date, and both from Massachusetts.