It was an elected position.
Governor Jeb Bush appointed Orlando Mayor Glenda Hood as Secretary of State effective February 2003. She leads the Department of State as it transitions from an elected constitutional office to an appointed Governor’s agency.
http://oss.dos.state.fl.us/background.html
Whether or not the SoS position in Florida is appointed or elected is immaterial. Someone who's job it is to conduct an election in a non-partisan fashion should not hold a partisan job in that election.