I've had an idea that I've been pinning to build for a while. I call it "the anachronism clock". The time piece is an old fashion pendulum. This is used to generate regular electrical pulses via point contacts. This signal would go to a series of electro-mechanical counters based on drums, motors, point contacts, and regions of non-conductivity. The counters would be arranged to output their position to mock nixie tubes built from LED's and plexiglass. Once an hour a tape recorder would be activated which will play a recording of the chimes of big ben.
Coming at it from the other side, not too hard to make a long-case ('grandfather') clock using the per-second signal from MSF (WWV, DCF etc) to drive the pendulum and so lock the clock to 'atomic' time.
An old 6 volt relay coil worked for me, main issue is needing a local backup oscillator stable enough to cope with period of signal loss/power outages.
Obviously simpler to use GPS 1PPS to derive the drive signal but that's a challenge to pick up with a coil of wire and a capacitor.
Definitely could be done; you'd also need an electromagnet to "pulse" the pendulum (much like the magnetic "perpetual motion" toys out there).
Also - I would suggest using regular bulbs instead of LEDs. If you can deal with the higher voltages involved, neon lamps would give it a great look.
Also, rather than a tape recorder, use one of those large doorbell "big ben" chimes instead (if you can find a really old one - from the 1960s or so - some of them used a similar motor/drum switched sequencer for the solenoid chime playing system).
It sounds very intriguing, and probably would be cool to watch function...
Another idea: synthesize a 32.768 kHz clock signal from the 1 PPS pulse of the pendulum by PLL, and use this clock to power a modern microcontroller to drive the 7-segment LEDs and show the current time.