In the rest condition, the voltage at pins 5 and 9 should be 12 V. Those pins pulse down to zero for about 1 second, causing the inverter outputs to go high and turn on the output transistors.
Referencing #22, in my troubleshooting I had been monitoring the voltage at pins 5 and 9. Pin 5 goes up to 6v. Pin 9 goes up to 8.5v. That's high enough to do the switching, but if it's supposed to go all the way to 12, then there must still be something wrong.