He doesn’t have to caucus with anyone. He can work with whom he chooses, when he chooses.
Serving as an “Independent” is a joke, because you still have to pick a side. You get an assignment from the caucus you choose or you go without portfolio (which then means you only vote on the floor, since you wouldn’t be serving in a committee. Not serving in a committee means you have no input in legislation, which then removes the sole reason for being elected to Congress).