Tony Jeffree started a thread on Lavet motors here:
https://www.model-engineer.co.uk/forums/topic/a-prototype-lavet-stepper-motor/
I found these two links I posted in the thread. The first patent describes a way to drive Lavet motors to do weird things such as make them go backwards and rotate faster to enable setting watches more easily:
https://worldwide.espacenet.com/patent/search/family/004292664/publication/EP0103542B1?q=pn%3DEP0103542B1
The second is a page by Tom Van Baak describing some measurements on those continuously rotating quartz clocks:
http://leapsecond.com/pages/sweep/
I suspect you have found one mode to make them go in reverse.
For another reason I recently wrote a simple routine for a Nano that reads a pot voltage between 0 and 5V (0 and 1023 binary), maps it to a range of desirable pulse widths (in my case 0 to 250ms), and generates a 1Hz pulse train with the selected value (which is printed out on the serial monitor), driving a MOSFET to switch the current to an electromagnet. Could easily be modified to drive a stepper via two output pins so one could explore how it behaves with different pulse widths.