Any person who holds full status in the classified service and resigns in good standing shall be entitled to have his or her name placed on an appropriate reemployment list, provided that the person so requests in writing within three (3) years of the date of his or her termination from the state service. Any person with full status who has resigned and whose appointing authority has failed to certify that he or she has resigned in good standing or any person with full status who has been dismissed from the classified service may request in writing within three (3) years of the date of his or her termination that his or her name be placed on the appropriate reemployment list and the request may be granted at the discretion of the personnel administrator. Each name placed on a reemployment list shall be stricken therefrom at the expiration of three (3) years from the official termination date.