How were Vice Presidents chosen from 1804 through 1824?

[darklordoftech]

In 1788-1800, whoever received the second-most Electoral votes for President became Vice President, and starting in 1828, Presidential candidates have had running mates, but what about in between 1800 and 1828?

[SamTilden2020]

They did have running mates.

https://en.wikipedia.org/wiki/United_States_presidential_election,_1804

[Unconditional Surrender Truman]

Candidates for vice president were selected by the party caucuses alongside the presidential nominee until 1820, when the collapse of the Federalist Party made such caucuses obsolete. In 1824, nominations were made by the state legislatures; John C. Calhoun got most of these (having dropped out of the crowded presidential race to seek the vice presidency) and is essentially the only person to have campaigned for the vice presidency independent of a presidential running mate.