§ 12-104. Electoral college; meeting and organization. The electors shall convene at the state capitol upon notice from, and at a place fixed by the secretary of state on the first Monday after the second Wednesday in December next following their election. Those of them who shall be assembled at twelve o'clock noon of that day shall immediately at that hour fill, by majority vote, all vacancies in the electoral college occasioned by the death, refusal to serve, or neglect to attend at that hour, of any elector, or any vacancies occasioned by an equal number votes having been given for two or more candidates. The electoral college being thus completed, they shall then choose a president and one or more secretaries from their own body.