This method is used by some Catholics, often Sedevacantists, who do not accept the legitimacy of their present papacy.
Conclavism is different from what George Chryssides calls the "mysticalists" phenomenon, i.e. people declaring themselves popes after receiving a personal mystical revelation.
[1] The description and explanation of conclavism of George Chryssides is:[1] Since most sedevacantists (although not all) object to Pope John XXIII's modernization of the Roman Catholic Church, they argue that he nullified his appointment to the papacy in 1958.
[1] In the late 1980s David Bawden promoted the idea of a papal election and ultimately sent out over 200 copies of a book of his to the editors of all the sedevacantist publications he could find, and to all the priests listed in a directory of traditionalists as being sedevacantists.
[2] He was then elected in 1990 by a group of six people who included himself and his parents, and took the name "Pope Michael".