Okla. Stat. tit. 22 § 601b
If, upon final submission of the cause, the court is of the opinion that the deliberations may be protracted, the court may order the alternate juror or jurors to remain sequestered physically or by admonition not to discuss the case with any person or allow any person to discuss the case with a juror. In such event said alternate or alternates shall remain apart from the jury and not take part in its deliberations, but shall await the call of the court at some place designated by the court until such time as said alternate may be needed. In the event one or two of the twelve jurors shall, during the course of deliberations, be discharged because of illness, or die, the court shall order one or both alternate jurors to take their places in the jury room and deliberations shall then continue.
In the event the cause is a bifurcated, two-stage proceeding, the "final submission of the cause" shall occur when the jury retires to deliberate upon the sentence in the punishment or second stage of the proceedings. In such a trial the alternates shall not be excused prior to commencement of deliberations in the second stage.
Okla. Stat. tit. 22, § 601b