Thanks, Frillmeister. One more thing: I actually forgot the most obvious part of this - the gong hammers for the repeater are displayed through the dial below the numbers. Doh. Black-polished, of course.
I had to read up on it later, but it has an interesting power system: moving the three time discs takes a lot of energy, and some of that is re-captured into a separate reserve to power the chimes; the energy from "braking" the discs when they've moved gradually draws back the hammer for the hour/quarter hour strikes. Therefore, winding the watch does not give the chimes power - it's the physical advancement under power of the time discs that does so. The extra pusher is to disengage the system if you don't want your watch chiming every fifteen minutes.
This is top level nerd shit. I am really finding it very pleasing.