The county conventions of each political party shall be held at the time and place that the county committee of each political party, through its chairperson, designates. County conventions at which delegates to a state convention are to be selected shall be held only at the times designated by the state central committee of the political party. The convention shall be called to order by the chairperson of the county committee of each political party. The chairperson shall act as temporary chairperson until the delegates elect a permanent chairperson. A permanent chairperson shall be elected before any other business is transacted. The election of a permanent chairperson shall be conducted as provided in this section. The chairperson of the county committee shall cause to be read the list of elected delegates and delegates at large under section 599(5) for the convention furnished to the chairperson by the county clerk under section 608. However, before reading the list, the chairperson of the county committee shall delete from the list the names of delegates that have been certified by the county clerk as disqualified under section 624a and shall add to the list the names of delegates elected to fill a vacancy for the balance of an unexpired term under this section, if any. When the name of each delegate on the list is called, the delegate shall state his or her choice for permanent chairperson. The person receiving a majority of the votes of the delegates present shall become permanent chairperson. The convention may fill any vacancy occurring in any delegation to a county convention by a majority vote of the delegates present. However, a vacancy shall not be filled by any person not a qualified, registered elector residing in the precinct in which the vacancy occurs. The convention shall prescribe the rules and regulations for the conduct of its affairs.