Though he received his name in that film, the puppet first appeared (sans eyepatch) in The Muppet Christmas Carol, taking on two different roles in the same film. In the opening number, "Scrooge," he plays a vegetable seller (of the Singing Food) performed by Frank Oz. Later on, in "It Feels Like Christmas," he resurfaces as a prisoner.
Although the character's name is One-Eyed Jack, and despite the presence of an eyepatch in Muppet Treasure Island, the puppet does not have any actual eyes as a facial adornment. Jack also appeared in Muppets Most Wanted.