Were I a Justice at SCOTUS...
The POTUS and VPOTUS candidates had been elected.
They only await either certification of the EC vote and inauguration or just inauguration.
If the POTUS elect is unavailable for whatever reason (not capable of performing the duties of the office), then it would fall upon the VPOTUS elect to either: serve until such time as the POTUS was again capable of taking office,
Or if that simply wasn't going to happen, to assume the duties of the POTUS, per the 25th Amendment and to nominate a new VPOTUS.
In the event of the demise of both simultaneously or nearly so, the office would fall to the Speaker of the House. (Again, the 25th)
Twice that I can recall, when Agnew resigned and when Nixon resigned and Ford took office, the office of VPOTUS was vacated and filled.
Nixon chose Ford as the new VPOTUS; Congress confirmed the choice.
When Nixon resigned, Ford moved up to POTUS, and nominated Nelson Rockefeller, who was also confirmed by a vote of both houses of Congress.
As the 25th had not yet been ratified during the Kennedy Administration, (not until 1967), the office of VPOTUS was vacant from the time LBJ was sworn in as POTUS (on the plane) until he was inaugurated as POTUS with Hubert H. Humphrey sworn in as VPOTUS.
