Sec. 12. (a) Before casting a vote, each freeholder must sign the list of freeholders opposite the freeholder's name in the presence of:
(1) the district secretary;
(2) the financial clerk; or
(3) a person designated by the district secretary or financial clerk.
(b) If:
(1) a clerk finds a freeholder's name is omitted from the list; and
(2) all three (3) clerks determine that the freeholder's name should be added to the list;
the clerks shall place the freeholder's name on the list and the freeholder may vote.