Eli was listed in the 1811 tax list for Cuyahoga County, Ohio. He was the Postmaster of Florence, Huron County, Ohio in 1828.
In the 1850 US Census for Florence, Erie County, Ohio the family of Eli S. Barnum was enumerated as follows:
Dwelling #190; Family #196
Eli S. Barnum, 68, M, Farmer Real property $4,000, b. Connecticut
Mary R. Barnum, 54, F, b. Massachusetts
Mary Barnum, 25, F, b. Ohio
Charly P. Barnum, 15, M, b. Ohio, Attended school within the year
Isibel G. Barnum, 11, F, b. Ohio, Attended school within the year
James Cowles, 35, M, b. Connecticut
Rhoda Cowles, 28, F, b. Ohio
Florence A. Cowles, 3, M [sic], b. Ohio