I thought he was one of Gardiner's sons, but he is the son of Luther Wait and Emily Bancroft as per his Civil War papers. He is born on 19 Oct 1840 in Sandy Hill, New York. I looked up Sandy Hill and found;
As early as 1792, the area of Kingsbury near Baker's Falls was referred to as Sandy Hill. In 1810, the hamlet incorporated as a village, keeping the name Sandy Hill. Its boundaries expanded to their current limits in the 1840's. In 1910, the village's name was changed to Hudson Falls.