In 1994, 1996, and quadrennially thereafter, when there is a political party which is a major party, as defined in subparagraph (A) of subdivision (5) of § 9-372, but is not a major party, as defined in subparagraph (B) of said subdivision (5), a percentage of the number of justices of the peace in each town selected under § 9-184c shall be selected in accordance with the provisions of this section. Such percentage shall be rounded down to the nearest whole number of justices of the peace. Each such party shall be entitled to nominate twenty per cent of the total number of justices of the peace to be selected in each town under § 9-184c. Such nomination by such parties shall qualify the nominees to serve as justices of the peace. Such nomination shall be made within the time limits prescribed in § 9-391 for endorsing candidates for nomination for municipal offices to be voted upon at a state election, for a term of two years to begin the first Monday of January in 1995, for any such nomination made in 1994, and for a term of four years to begin the first Monday of January in the year succeeding any such nomination made in 1996, or thereafter. Primaries for justices of the peace shall be by slate and shall be held on the same day as primaries for municipal offices to be voted upon at a state election.