Gladstone is an unincorporated layover in Union County, New Mexico, United States, founded in 1880. It lies at the intersection of US Route 56 and Union County Road C001. The post office, which opened in 1888, closed in 2010, leaving only a general store with gas service, and two houses, located there. The rest of the community has reverted to priv…Gladstone is an unincorporated layover in Union County, New Mexico, United States, founded in 1880. It lies at the intersection of US Route 56 and Union County Road C001. The post office, which opened in 1888, closed in 2010, leaving only a general store with gas service, and two houses, located there. The rest of the community has reverted to private ranch land.