When judgment of death becomes final and a writ of certiorari to the United States Supreme Court has been denied or the time for filing such petition has expired, the court shall set an execution date for a person sentenced to the death penalty. Within sixty (60) days following the appointment of post-conviction counsel, upon declaration by counsel that he deems post-conviction review to be meritorious and that he intends to file an application for post-conviction review, the court may stay execution pending the disposition of the post-conviction proceeding. In the event no application for post-conviction relief is filed within one (1) year of the date of the disposition of the petition for writ of certiorari or the time for certiorari has expired, any stay entered by the court will automatically vacate. The filing of a declaration by counsel that he deems post-conviction review to be meritorious and intends to file an application for post-conviction review shall in no manner constitute the filing of an application for post-conviction review that would toll the running of any statute of limitations. Setting or resetting the date of execution shall be made on motion of the state that all state and federal remedies have been exhausted, or that the defendant has failed to file for further state or federal review within the time allowed by law.