Section 60. If the commissioner or commissioners, or any of them, designated in the petition, file with the village clerk, within five days after the last mentioned notice from the village clerk, his or their written resignation, the village clerk shall at once notify the election authorities of the fact; and such resignation shall be irrevocable and the vacancy shall be filled according to the provisions of section four of this charter. In the absence of any such resignation the election authorities shall forthwith order and fix a day for holding a recall election for the removal of those not resigning. Any such election shall be held not less than thirty nor more than sixty days after the expiration of the period of five days last mentioned, and at the same time as any other general or special election held within such period; but if no such election be held within such period the election authorities shall call a special recall election to be held within the period aforesaid.