The members of the Authority shall be appointed by the Governor, who shall give notice of the member’s selection to each other member within 10 days after selection and before the member’s entering upon the duties of office. Three of the members shall be appointed by the Governor from a list of 4 candidates provided by the mayor of the City of Dixon, and 2 of the members shall be appointed by the Governor from a list of 3 candidates provided by the chairman of the county board of Lee County. Each member of the Authority shall take and subscribe to the constitutional oath of office and file it with the Secretary of State. If a vacancy occurs by death, resignation, or otherwise, the vacancy shall be filled by the Governor. All appointments of members shall be for a 3-year term. Each member shall continue to serve an additional 3-year term unless that member is replaced by appointment within 60 days of the end of his or her term.