Unfortunately, there were few records for the 13th Battalion/5th Regiment that survived the war. Have you seen his full military service record? The Booth books do not include everything from them. It is possible that there is a document or two in his record that would show his rank as a 1st Lieutenant. Looking at what Booth shows, he probably would not have been "elected" to that rank. Elections pretty much ended in 1862. He would simply have been promoted as other officers moved up in rank or left the unit.