Mike, I found Squire and family in an 1885 state census for Logan TWP, Butler County, Kansas, and in Justice Precinct 4, Kaufman County, Texas, in 1900. We learn from the Kansas State Census that Squire was born in Elizabethtown, Kentucky, which is in Hardin County.
He appears in the 1850 Census for Spadra TWP, Johnson County, AR, living in the household of Laben and Lydia Wright. Laben Wright was living in Hardin County, KY, in 1840, so Lydia was possibly Squire’s mother and Laben was his stepfather. Lydia was born in VA, and in 1900 Squire gave his mother’s birthplace as VA.