When someone is both serious and joking, with the deciding factor being how people react. Often times they are serious, but if people react in a way that they did expect or foresee, a Schrodinger's Jester will claim it is a joke.
Person A: "I am a pacifist until I get angry"
Person B: "That isn't how being a pacifist works"
Person A: "Yes it is!"
Person C: "It actually isn't"
Person A: "It was a joke"
In this scenario, Person A was a Schrodinger's Jester