The optimum condition for the success of a third party is general dissatisfaction with established political parties and/or their policies on one or more issues. The most successful third party in American history was the Whig Party, formed in 1832 from two existing third parties (the National Republican Party and the Anti-Masonic Party). The Whigs were composed of a diverse group of supporters, who had little in common except for their opposition to Andrew Jackson and Martin Van Buren. The Whigs successfully elected two presidents (William Henry Harrison and Zachary Taylor), and the party's ranks included a young Abraham Lincoln. The Whigs fielded their last presidential candidate (General Winfield Scott) in 1852; the Whigs subsequently became part of the newly-founded Republican Party, which still exists.
In 1948, Strom Thurmond's States' Rights Democrats won a handful of Southern states in the general election; in that same year, former Vice-President Henry Wallace led the Progressive Party, but captured no electoral votes. In 1968 Alabama Governor George Wallace's American Independent Party captured 13 electoral votes, but was not a factor thereafter. Thurmond ran on a pledge to continue segregation, Henry Wallace ran on a platform which called for peace at any price with the Soviet Union, and George Wallace's campaign was based on "law and order", and also appealed to the segregationist element.
I hope this helps.
Content will be erased after question is completed.