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 Co Court record, and had 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.