I don't think this is the most natural interpretation of the Joker. I would opt for rules where the Joker keeps mimicking the previously moved piece after null move (just as it would after opponent Joker move). But that for implementation of the 'castling through check' rule the partial-move interpretation would be used: would the King be capturable if it only performed the move up to that point? The castling issue is not only relevant to the Joker. E.g. with a lame Dababba (nD) on d1, could you play O-O? I would say 'no', because after the King steps to f1, the nD could capture it. But with the King still on e1 the nD cannot capture to f1.
[Edit] Another interpretation could be that the Joker during the opponent turn it always moves as King (or whatever royal you have). A null move cannot be unambiguously assigned to any piece, but for the definition of check we could use the fiction that the royal must make it, in contexts where it matters what piece was moved.
Of course it is still a matter of taste what the Joker imitates after castling. If we consider castling a 3-step move (K+K+R), it would be most natural if it imitated the Rook.
I don't think this is the most natural interpretation of the Joker. I would opt for rules where the Joker keeps mimicking the previously moved piece after null move (just as it would after opponent Joker move). But that for implementation of the 'castling through check' rule the partial-move interpretation would be used: would the King be capturable if it only performed the move up to that point? The castling issue is not only relevant to the Joker. E.g. with a lame Dababba (nD) on d1, could you play O-O? I would say 'no', because after the King steps to f1, the nD could capture it. But with the King still on e1 the nD cannot capture to f1.
[Edit] Another interpretation could be that the Joker during the opponent turn it always moves as King (or whatever royal you have). A null move cannot be unambiguously assigned to any piece, but for the definition of check we could use the fiction that the royal must make it, in contexts where it matters what piece was moved.
Of course it is still a matter of taste what the Joker imitates after castling. If we consider castling a 3-step move (K+K+R), it would be most natural if it imitated the Rook.