Gold Star Fathers Act of 2013 - Includes as a preference eligible for federal employment purposes a parent (currently, the mother only) of either an individual who lost his or her life under honorable conditions while serving in the Armed Forces during a war, in a campaign or expedition for which a campaign badge has been authorized, or during the period beginning April 28, 1952, and ending July 1, 1955, or a service-connected permanently and totally disabled veteran, if: (1) the spouse of such parent is totally and permanently disabled; or (2) such parent, when preference is claimed, is unmarried or legally separated from his or her spouse.