At any stage thereof any action or proceeding in any court in which a person in military service is involved, either as plaintiff or defendant, during the period of such service or within 60 days thereafter may, in the discretion of the court in which it is pending, on its own motion, and shall, on application to it by such person or some person on his behalf, be stayed as provided in the act of October 17, 1940, known as the Soldiers' and Sailors' Civil Relief Act of 1940 (54 Stat. 1178, 50 U.S.C. app. § 501 et seq.), unless, in the opinion of the court, the ability of the plaintiff to prosecute the action or the defendant to conduct his defense is not materially affected by reason of his military service.