The governor shall submit the name of the two (2) members of the board whom he or she desires to appoint and who are not of the same political party as the governor to the chairperson of the state central committee of the party of which that person is a member for the approval of the chairperson. If the chairperson shall disapprove the names submitted to him or her, the governor shall submit another name, and so on in like manner until approval is obtained; provided, however, that if no disapproval is made within five (5) days from the submission of a name by the governor, the name of the person to be appointed shall be deemed to have been approved. Thereafter, if an appointment is to be made to the board of a member who is not of the same political party as the governor, the appointment shall be made as above provided.