Hoyt Weathers thought it a good use of my time to say:
Wow! I wish there was a newsgroup where this was on-topic! More "space
math" than I have seen in a long time. The way I see it, though,(like you
really want to know) is that the issue has been "under simplified". The
clock works through the use of (a) falling weight(s). This weight has its
"weight" based on the total force required to overcome the
friction/inertia/gearing needed to move Mickey's hands around the clockface.
If the moon's gravity is .XXX times the earth's gravity, then that clock
will move .XXX times slower on the moon. AFAIK, there is no other
weight-save the pendulum(which is "driven" by the rate of the falling
weight), and therefore there is no additional 'gravitational' requirement,
only the torque needed to spin the gears.
But, I could be full of it, and not know!