Should the contestant at any time during the proceeding desire that the recount be terminated, he may announce the same to the county election board. In such event, the recount shall end at that point, and any changes be made a part of the certificate of vote. Provided further, however, that should any contestee desire that the recount continue, he may petition in writing at the time of said announcement for the remainder of the ballots in that county to be recounted. Said petition must be filed immediately with the county election board conducting said recount, and petition must be accompanied by either a cashier's check or certified check in an amount equal to the deposit made by the contestant to conduct the recount. If said recount was ordered by the Secretary of the State Election Board, said check shall be transmitted forthwith to the State Election Board. In the event contestee files such petition, the recount shall continue until such time as all the ballots in said county have been recounted, and the recount is complete. Recounts of issue or question elections shall not cease until all precincts and absentee ballots in the designated county or counties have been recounted.