I would guess the Infallible trigger is an after market on your gun. I have a very late Lefever, probably assembled at Ithaca which has an Infallible trigger on it. This one may have been there when built or may not have. The trigger is selectable but does not reset upon opening the gun. Thus if one bbl only is fired & then gun opened & reloaded it will still fire the opposite bbl on next trigger pull unless manually reset. The selector slide on the tang moves to the other position with each trigger pull.
