Cuckoo clock type mechanism - looking for suggestions

I’m trying to see if I can build this relatively easy. I want to make a mechanism which moves a small figurine out of a cage and then back in, closing the cage door behind it - just like a cuckoo clock. What I’m thinking of is a mechanism similar to this cuckoo clock:

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ie. the figurine is on a caddy which is linked to the door by pivots, which slot into cutouts in the caddy itself. In my use case the caddy would be driven from below by a belt attached to a stepper motor. The figurine should ideally be able to slide past the door a bit (but I think I could just make the caddy longer for that)

Is this viable? What other ways can I build this?

Hi, the original cuckoo clock had a return pivot mechanism (forward , reverse gearing ) maybe a motor that can travel on a rail type system with a return button at each end ,one to send it back and the other to make it stop or pause, I hope this is of some help. Brian