What is the test for substituting an alternate juror during jury deliberations?

[T]he presence of an alternate juror in the jury room ... "destroys the sanctity of the jury." United States v. Beasley, 464 F.2d 468, 470 (10th Cir.1972). The mere presence of the alternate may well have an effect on the deliberations of the twelve....

When an alternate is present in the jury room, thereby violating the privacy of jury deliberations, a problem of constitutional dimension arises. There is thus greater justification for a rule of reversal per se where an alternate is present during deliberations ... than where an alternate is substituted after deliberations have commenced. See Leser v. United States, 358 F.2d 313, 318 (9th Cir), petition for cert. dismissed, 385 U.S. 802, 87 S.Ct. 10, 17 L.Ed.2d 49 (1966).