On January 12, American Third Position announced that it had nominated its first candidates for President and Vice-President. They are Merlin L. Miller for President and Virginia Deane Abernethy, both of whom live in Tennessee. Thanks to Independent Political Report for this news. The party is not now ballot-qualified in any state.
Miller is an independent film maker and Abernethy is a retired professor of psychiatry and anthropology. Abernethy was born in Cuba, but presumably her parents were U.S. citizens. See here for more information about her.