[No record of Jeremiah is found in Haverhill tying him to this family, but he is presented that way in this source, and since he appears to be one of the principal persons covered under the surname Pecker, this has been used. He clearly appears to fall nicely into a gap between known children. The marriages and births (though not the death) appear to show up on familysearch.org as given in this source, and in the 1840 Census, Jeremiah is listed in Concord, NH, age 60-70, so born 1770-1780.]
Captain Jeremiah Pecker, s/o Dr. James Pecker and Susanna Cogswell [sic, see following comment], b. Haverhill, d. 12 Aug 1843 age 71, m. (1) Concord NH 12 Mar 1779 Ruth Kimball, m. (2) Mary (Eastman) Lang.
[Note: Stears was pretty sloppy as the age at death he gives results in a birth estimate of 1772, and the passage on the father that Stearns himself has shows his second marriage occurring in 1761. So he clearly has Jeremiah attributed to the wrong mother.]