There shall be a thirty-day enrollment period, at a time designated by the board, during which retirees and surviving dependents of retirees or employees of a participating member agency who are not then covered by any health care plan offered by the participating member agency shall be able to enroll in the plan upon provision, at their^* own expense, of evidence of good health satisfactory to the board. A preexisting condition will not be covered until a person has been a plan participant for a period of twelve consecutive months.