The board shall make and keep a register of all persons eligible and available for appointment to each class of position in the service of the city. No examination shall be given and no register kept for positions to be filled by persons designated by the board as laborers. Layoffs available for re-employment shall be placed at the head of the proper present and subsequent eligible registers in the inverse order of their terminations. Employees who voluntarily terminate their services may be granted re-employment status upon proper eligible registers under the circumstances and in the manner as may be provided for in the rules and regulations of the board, subject to stipulations of this section concerning layoffs. Persons desiring appointment may file applications with the board, and the board, from time to time, may conduct examinations to test the ability of the applicants if requested by the governing body. All applicants shall be reviewed and determined by the board to be qualified or unqualified based on the applicable job description. Should the governing body request that the applicants for a particular position be examined, the examinations shall be public, competitive, and subject to the limitations specified by the board, and approved by the governing body, as to age, residence, health, height, weight, habits, moral character, and other factors pertinent to the ability to discharge the duties of the position. The board shall fill vacancies in the classified service, insofar as practicable, by promotions from among regular employees holding positions in the classified service. If the board decides to fill a vacancy within the classified service, the board shall determine the regular employees holding the classified positions in the department or departments eligible to take the examination. Examinations shall be practical in character and shall relate to those matters which test the ability of the person examined to discharge intelligently the duties of the position for which he or she applies. In no case shall an appointment be made from an eligible register which is more than one year old.