My first two ideas for controlling the clock were: to keep the clock's circuit entirely intact and just turn its power on and off with a GPIO on the ESP8266, or to remove the crystal and provide a wave from the microcontroller at a frequency based on how slow I needed the clock to move. The first idea did not work well because the movement of the hands with a one second pulse of power would vary unpredictably, making the clock very inaccurate. The second idea worked considerably better, but required more work from the microcontroller as it had to be putting out a wave constantly. It also lost accuracy pretty quickly. So, I went one level deeper into the clock and bypassed the internal circuits entirely, controlling the clock's motor directly from the microcontroller.