In the case of a tie, the candidates receiving the tie vote shall cast lots before the county board or the Secretary of the Commonwealth, as the case may be, at twelve o'clock noon on the third Friday following the primary, and the one to whom the lot shall fall shall be entitled to the nomination. In any case where the fact of a tie vote is not authoritatively determined until after the third Wednesday following the primary, the time for casting lots shall be at twelve o'clock noon on the second day after the fact of such tie vote is authoritatively determined. If any candidate or candidates, receiving a tie vote, fail to appear before twelve o'clock noon on said day, the county board or the Secretary of the Commonwealth, as the case may be, shall cast lots for him or them. For the purpose of casting lots any candidate may appear in person, or by proxy appointed in writing.