No person shall at the same time hold the office of judge or substitute judge of a district court and the office of magistrate, clerk of a court, sheriff, treasurer, or commissioner of the revenue, or deputy of either of them. A full-time district court judge may not serve as a commissioner of accounts, commissioner in chancery or a marriage celebrant appointed by the circuit court pursuant to § 20-25, nor shall such judge, during his continuance in office, seek or accept any nonjudicial elective office, or hold any other office of public trust or engage in any other incompatible activity. If any judge of a district court shall accept any office for which he is ineligible under this section, such acceptance shall vacate his office as judge of such court.