Except as hereinafter provided, vacancies in positions in the classified service shall be filled by the appointing authority by the appointment of a person whose name is certified, within 30 days after certification. Certification shall be made upon the request of the appointing authority therefor whenever a vacancy exists, the appointing authority, in his or her discretion, determines that such vacancy shall be filled, and the name of an applicant for such vacancy is eligible for certification. If there is a laid off person on the reemployment list with respect to a vacancy, only the top name on such list shall be eligible for certification. In the event the top person is not available for appointment, the next ranking names may be certified until the highest ranking person who is available is appointed. In the event there is no such reemployment list, and the names on the promotional eligible list for such vacancy plus the names on the original appointment eligible list for such vacancy equal three or more, the three names ranked highest on the promotional eligible list shall be eligible for certification; provided, however, should the promotional eligible list not contain three names, then the names appearing thereon, plus such of the names ranked highest on the original appointment eligible list as shall be sufficient to bring the number of certified to three shall be eligible for certification. If after making reasonable effort it should prove impossible for the appointing authority to locate any of the persons so certified or should it become known to the board that any person so certified is not willing to accept the position, the appointing authority may request that additional names be certified until the appointing authority has available to him or her a list from which to make the appointment containing the aforesaid authorized number of persons all of whom are available for such appointment and willing to accept the position, or, in the event that the list certified to the appointing authority contains fewer than the authorized number of available and willing persons as aforesaid from which to make a selection, the appointing authority, in his or her discretion, may choose from the remaining certified names, make a temporary appointment, or make no appointment. In the event that there does not exist an employment list which the board deems to be appropriate from which to fill the vacancy, the board shall prepare such a list within a reasonable time after receipt of the request of the appointing authority that eligibility be certified. Provided, however, nothing herein contained shall be construed as preventing an appointing authority, in his or her discretion, from withdrawing his or her request for the aforesaid certification, either before or after such certification has been made in response to his or her request therefor. Whenever a person has been certified to and rejected by an appointing authority three times, the board may remove the name of such person from the eligible list on which his or her name appeared. A person shall be deemed to have been so rejected by an appointing authority when a vacancy is filled from an eligible list on which his or her name appeared and such person was not selected to fill the vacancy.