I'd originally started this project as a tortoise popping in and out of her shell but, having put the mechanism together, it reminded me of a chameleon rocking back and forth on a twig.

The model has a pendulum in the lower part of the box with a relatively heavy weight. (Four coins in this case)

I'll be replacing the vertical linkages with legs and adding  suitable head and tail. I can still come back and use the mech for a tortoise, or a dog in a kennel at a later date.