I was able to drive the clock last night. Unfortunately even with the resistor recommendations it didn't have enough current to force a tick over. So what I ended up doing is putting a potentiometer in series and adjusting down until I could get it going with the final outcome being a 100 ohm resistor in series with the MCU pins. I have to short the resistor to get it to start moving the gears and then remove the short so it can continue off of the 100 Ohm resistor.
The pulses I ended up with are to invert every 18ms. 17ms seems to have a little trouble starting sometimes, but 18 seems stable. As of yet I haven't figured out a way to control the direction other than repeatedly resetting the power or tapping the second hand while it is in motion to cause it to change direction.
At the current rate of speed the minute hand moves at about the rate the second hand used to move.
I suspect the original wave form had something to do with keeping it in the same direction all the time. I'm pretty much using a square wave right now, but I haven't scoped it out yet.
When I was looking at the original wave form, it looked sort of like this. (Not to time scale)
So the upside had a curve up and the down side had a curve down. Due to the slowness of the spacing I can't get the up and down curve on my analog scope on the same screen. That's also the reason I don't see a vertical line, it just shuts the power off at the end.