Before any person is entitled to retirement benefits under the provisions of this article, he or she shall submit proof of his or her eligibility for retirement benefits to the Governor. If the judge is still sitting, he or she shall at the same time tender to the Governor his or her resignation as judge to the Governor upon condition that, if the resignation is accepted, he or she will be paid retirement benefits as provided in this article. Upon request for retirement by a sitting judge, the Governor shall investigate to the extent he or she deems advisable to determine the judge's eligibility. If the Governor determines that such person is entitled to retirement benefits under the provisions of this article, the Governor shall accept the resignation and certify the facts and the amount of retirement benefits to be paid to the judge upon retirement by a written order filed in the office of the Secretary of State. The Secretary of State shall, upon receipt of the order, file a certified copy of the order with the State Auditor, the Governor's office, the Supreme Court of Appeals' administrative office and the Consolidated Public Retirement Board. After accepting the judge's resignation, a vacancy is created in the office of the retiring judge which shall be filled by appointment or election as provided by law.