Thank you much for the reply. Your second reference is, actually, my own website. The next update for Eleazer is already in the database (to be posted sometime this week probably) as follows:
"Encyclopedia of Connecticut Biography has Eleazer moving to Connecticut after wife Anne's death (no reference for her death or his emigration), and marrying there May Markham. Neither Sprague nor Hillman lists Eleazer's marriage to May Markham. Connecticut Town Birth Records, pre-1879 (Barbour Collection) has (Middletown Vital Records 1651-1854) Eleazer m 1745/6 Jan 20, Mary Markham. Other records in that collection have children and their marriages. The main question is whether Eleazer did, in fact, emigrate to Connecticut and marry Mary Markham. If his wife Anne died soon after co-signing a deed with him in 1743 (her last occurrence in the records according to Hillman), he may well have had reason to leave the area. He had been involved in 1741 and 1742 in actionable behavior, according to Plymouth County Court records, and had even been confined in the Boston jail for debt. In addition, on Oct 23, 1741 (per Braintree First Church records), he was suspended from communion for "disorderly unchristian life.." Further research may uncover more of his story."
FYI - "Hillman" is Ralph Hillman who earlier this year published Veazie Genealogy, an extremely well-researched work of some 700 pages. Sprague is, of course, THE Sprague.
Your first reference has his suspension from communion as Oct 25. I'm not sure whether the author or myself got it incorrect, but it's certainly immaterial.
Unfortunately, everything I have so far is circumstantial and I'm looking for some more solid reference to convince myself.