Something I hadn’t realized until today was that there was no Vice President, until LBJ was elected and was inaugurated in 1965, when Humphrey became VP.
Until the 25th Amendment's adoption in 1967, that was true every time the VP became President, resigned, or died. The office remained vacant until the start of the next term. Under Section 2 of that amendment, the President nominates a new VP who takes office if confirmed by the House and Senate. This was done twice during Watergate.