Eliseo lives in Milan, NM with his wife Darlene. Representative Alcon has one son, David, and one daughter, Annette. He is a disabled veteran and retired Magistrate Judge.
Eliseo is working on legislation to fund Native American schools as equally as other schools. Representative Alcon has been serving in the New Mexico House of Representatives since 2009, and currently Chairs the House Consumer and Public Affairs Committee and is a member of the House Judiciary Committee.