Internet searches turned up quite a few clock projects.  Many were digital and while interesting did not help much.  Quite a few were complete custom clocks.  I did find a few Analog Clock hacks.

   I found two that was were similar to what I wanted: (http://hackaday.com/2015/11/19/a-networked-analog-clock/ and https://hackaday.io/project/16742-espclock.). The problem for me was I wanted battery operation and the ESP8266 cpu/wifi module uses 70 milli-amps on average - much too much for the battery powered device I wanted.      Another interesting one I found was “Crazy Clock”: (https://hackaday.io/project/5880-crazy-clock). This remained lower power but had no network connectivity to keep the clock synched with an external time source. It did however had a really nice description on how standard quartz clock movements work.    And another, "Lunchtime Clock": (http://www.instructables.com/id/Lunchtime-Clock/)).  It uses a RealTime Clock module to keep accurate track of the correct time.  This one also uses too much power and does not have network connectivity.

   So I went shopping with the wife and bought two fairly cheap ($10) analog clocks and survived "the look" when I immediately disassembled them upon arriving home.

 Most quartz clock movements use a Lavet type stepping motor to physically drive the clock hands.  Driving one of these requires us to alternate polarity each second. This can be done with a half H-Bridge type of circuit.