Okay, so I've established that I can use a linkages to magnify the motion of a pendulum. Time to try and fit it into a neatly set out box that can be used in a completed character model.
I've set the pendulum so that it is swinging back and forth in the box hinged at a hole in the top of the box with a paper hinge to reduce friction. Again, I've used a couple of coins for the weights. The linkage between the pendulum and the tail now has a ninety degree twist so the tail can wag side to side.
That'll do nicely! Next step: wrap a body and head round the mechanism.