Notwithstanding the provisions of any special act or charter to the contrary, whenever any person makes application for admission as an elector in person to an admitting official, he may, on an application for admission as an elector, make application for enrollment on the list of the political party of his preference. Any such elector who has so applied for enrollment shall, upon acquisition of electoral privileges, immediately be entitled to all the privileges of enrollment in the party named in his application, unless (1) he ceases to be an elector in the town or voting district in which he is entitled to vote, as the case may be, (2) he makes application for erasure or transfer or enrollment on the list of another party in accordance with the provisions of § 9-59, (3) he files his application for enrollment with the registrars of voters of his town of residence after twelve o’clock noon on the last business day before a primary, in which case he shall be entitled to the privileges of party enrollment immediately after the primary, or (4) he files his application for enrollment with the registrars of voters of his town of residence on the day of a caucus or convention, in which case he shall be entitled to the privileges of party enrollment immediately after the caucus or convention. The registrars of voters or assistant registrars shall add the names of all persons making such application to the enrollment list or supplementary enrollment list of the political party of each such applicant’s preference, provided, if a caucus or convention is to be held, such registrars or assistant registrars shall prepare separate lists of such names according to party, on the day before such caucus or convention.