A Civil War pension indicated the soldier was born in Duncansville, Kentucky. As I suspected it was not on a modern map. There are several ways to locate a place name that no longer exists–one way is to search for it on GoogleBooks where old books have been digitized are full-text searchable.
An 1889 reference to the change in the Mercer-Washington County Kentucky line mentioned Duncansville. That gave me a clue as to it’s location.