In each county, the name of each candidate for member of central committees shall appear on the ballot only if she or he has done either of the following:
(a) Filed a nomination paper pursuant to Article 2 (commencing with Section 8020) to Article 6 (commencing with Section 8100), inclusive, of Chapter 1 of Part 1 of Division 8, signed in the candidate’s behalf by the voters of the central committee election district in which she or he is a candidate.
(b) Qualified to have her or his name printed on the direct primary ballot as a candidate for the Peace and Freedom Party nomination to a partisan public office.