[https://www.youtube.com/watch?v=IiTdEuQiMXg|This video] might give you some idea of the inner workings, at least in principle. They get into it using a Dremel, which I assume is not how you plan to get into your Jack-In-The-Box.
[https://www.youtube.com/watch?v=sbbDUEMRej0&t=6m17s|This old video] shows how they used to be put together, which might still be relevant and provide a clue as to how to open it.
However you do end up getting inside, might I suggest documenting it and posting it as a guide on the device page? https://www.ifixit.com/Guide/new/Device/Jack-In-The-Box
Good luck!