The court may, for good cause shown, continue an action at any stage of the proceedings upon terms as may be just; provided, that if a party or his attorney of record is serving as a member of the Legislature or the Senate, sitting as a court of impeachment, or within thirty (30) days after an adjournment of a session of the Legislature, such fact shall constitute cause for continuance of the case, and it is mandatory that the court shall grant such continuance upon motion whether such attorney may have been employed before or during the session of the Legislature, and the court shall have no power to exercise its discretion as to the granting of such continuance, and all motions, demurrers and preliminary matters to be heard by the court, the refusal to grant which shall constitute error, and entitle such party to a new trial as a matter of right. When a continuance is granted on account of the absence of evidence, it shall be at the cost of the party making the application unless the court otherwise order. And when any litigant has given notice of appeal from any judgment of any court of record in this state to the Supreme Court or Criminal Court of Appeals and the time for doing any act to perfect such appeal has, or does hereafter lapse during the session of the Legislature, whether regular or special, and the said litigant is a member of the Senate or House of Representatives, of the State of Oklahoma, in such session, or his attorney of record is such member, such litigant or attorney shall have such time after the adjournment of the session of the Legislature to perform such act and complete his appeal as he had at the commencement of the session of the Legislature, of which he or his attorney of record was a member, and all acts done in the perfection of such appeals shall be as valid as if done within the time provided.