I think the main problem with a mechanical pulse generator would be keeping it synchronized to the 0.5 Hz internally generated drive signal for the separators. It would require some sort of frequency locked loop to regulate the motor driving it. It would drive me crazy looking at an out of sync mechanical apparatus that's supposed to look like it's the timing source for the clock. It could be built, but it requires a great deal of determination to design and implement the circuit to sync everything.
I'm picturing something involving a synchronous motor, a gear train and a cam. Cam lifts some sort of "hammer" and drops it once per second. When it drops it hits a contact or maybe hits a switch? Might look cool behind a glass window or something. I'm just thinking out loud,
Look into it later when the dust is clearing off the crater.
Now you've got me thinking along the silent operation lines. What if we could get a 1-minute egg timer (hourglass type) device, and have a motor flip it once a minute? That would give you a visual representation of the minute passing by the sand filling the lower glass.
I will be using a 50Hz synchronous mains motor. In the UK This frequency by law has to be within 1% and is more accurate long term. I have found one motor with a speed of 10RPM and 6 divisions will give me the 1Hz I need
The idea I am playing with at the moment is a 100mm disc fitted to a 10 RPM synchronous motor. Around the edge of the disc I have countersunk 6 magnets. Imagine a waterwheel set up and you wont be far wrong. The disc rotates anticlockwise and each magnet picks up a ball bearing at the bottom, the ball then rises up and travels past the 12 o'clock where a guide dislodges the bearing which then falls back down to the bottom in a guide. So, 6 magnets and 6 balls with a sensor somewhere in line where the balls fall should give me my 1 second pulse.