Except as provided below, any person appointed under Section 3-5 shall hold no other lucrative public office or public employment. In counties with less than 100,000 inhabitants, he or she may hold public employment if the duties are not incompatible with his or her duties as supervisor of assessments as assigned by the county board. The duties of a person administering a county zoning ordinance shall not be considered incompatible with the duties of a supervisor of assessments.