When does a nominee to the US Supreme Court become a member of the court - immediately upon confirmation vote by the senate or only after swearing in - what if SCOTUS is in recess?

A nominee receives his or her commission upon vote of Senate, but doesn't become a member of the Court until he or she takes the Oaths of Office. The Supreme Court requires justices take two separate Oaths, one is Constitutional, the other Judicial.

It seems inconceivable that the Chief Justice or Senior Justice would be away when a new justice is due to be sworn in, but I suppose if no one were available to administer the Oath, there would be no pressing business on the Court docket, and the new Junior Justice would take the Oath(s) of Office at the first available opportunity.