I reseated a cable and tested things again, being careful.
   It turns out the multimeter is sometimes giving a bit of a delay before
   showing the 12v voltages, showing 0 while the wire touches 12v for half
   a second or so.
   Anyway, the motor turns now!
   I have not yet reversed it to unwind the cord, taped the relays back
   on, nor labeled the other board as broken.
   I get the impression it might be nice to have test points of some sort
   to debug stuff. I have some wire-in voltmeters from another project.
   Not sure.