Got a Kienzle clock of the same size that works. Strangely, the second hand moves at a smooth rate, rather than jumps per second like the original.

On slight problem was that it was meant to be mounted vertical. So I took them both apart and swapped the dial over from the original. they were not quite the same size and the light was in a different location, but the adjustment knob was the same.
To make the original dial fit, I had to remove the plastic taps that held the new dial. Then I glued the old dial onto the plate and assembled everything.
Works great and looks good.
