DAR is wrong about his birth location. He was born in Chebacco parish, Essex county, Mass. Now called the town of Essex. Then, part of Ipswich.
This is Andrew Burnham's father:
https://www.wikitree.com/wiki/Burnham-454
His brother Isaac is already here on Wikitree tree. Ebenezer moved from Chebacco parish to Windham CT with his children; and bought a farm there circa 1774. I don't know when he moved, though.
Coincidentally, Ebenezer's father John is my direct ancestor. In a further coincidence, Andrew's patriotic service was selling stuff to the CT regiment my direct Taylor ancestor served in.