Notwithstanding any other provision of law to the contrary, any member of the general assembly and any elected state official holding a statewide elective state office, who ceases to hold elective office, or any person employed by the elected official or employed by a member of the general assembly, whose employment is terminated because such elected official or member of the general assembly ceases to hold elective office, may elect to continue insurance benefits to cover medical expenses provided under sections 103.003 to 103.175, by paying the cost of such benefits as determined by the board. If an eligible person does not elect to continue the coverage within thirty-one days from the last day of the month in which the eligible person ceases to be an employee, he may not later elect to be covered under this section.