Having this memory I decided to surf the internet to see if wooden gear clocks still existed.
I found someone who was making some gears.
Much to my surprise I found a site that sells plans to make such clocks. I could not find one that looked like the clock we had but I found some very very interesting designs.
The creator also has a short YouTube video sowing the clocks in action.
The best video of all is this one about using shop tools to make a clock.