Speeding up an analog clock
Usually 32768Hz quartz crystals are used in the clock applications. This standard is very widespread and these crystals are cheap and highly easy to find.

In order to switch the clock to work twice as fast, you will need 65536Hz crystal, that is not standard, not so common and probably not so easy to be purchased. For example my local distributor has 32768Hz crystals on $0.1 each and the next frequency available is 1.8432MHz

Another possible issue is the work of the internal oscillator with the changed crystal. It will probably work, but some capacitors might need to be replaced with other values.

And at the end, the last possible problem is the stepper motor of the clock. Is it capable of stepping twice as fast as usual?