Each petitioner shall, upon affixing his signature to the petition for termination, write in the date of signing. No signature to the petition shall be valid for any purpose if affixed more than six months prior to the filing of the petition with the director. The petition shall be accompanied by a good and sufficient undertaking in an amount which is equal to the probable costs incident to conducting the hearing and making of findings. A hearing shall be held by the director upon the petition to determine the sufficiency of the signatures within 60 days after the presentation of the petition.