The Attorney General, Chief Financial Officer, and Commissioner of Agriculture shall reside at the capital, and no member of the Cabinet shall absent himself or herself from the state for a period of 60 consecutive days or more without the consent of the Governor and a majority of the Cabinet. If a Cabinet officer should refuse or fail to comply with and observe the requirements of this section, his or her office may be deemed vacant pursuant to paragraph (f) or paragraph (g) of s. 114.01(1), as appropriate.