When a vacancy occurs in the statutory or appointive membership of the council, the presiding officer of the house incurring the vacancy shall fill the vacancy within 30 days. If the office of the president of the senate or speaker of the house of representatives becomes vacant and a vacancy occurs among the appointed members of the council, the remaining council members from the house incurring the vacancy shall appoint a new member. A legislator appointed to fill a vacancy shall be a member of the same political party as the member vacating the seat, when possible.