Thanks. I solved the mystery almost by accident.
With the ignition on but engine not running I heard a loud buzzing tone from under the hood. It turned out to be the blower relay under the air box, which was oscillating on and off rapidly. This is the main blower relay. I swapped it with the adjacent high blower relay. The noise stopped. Then I replaced fuse 10 and it did not blow. I plugged in the heater door actuator and it worked.
Looking at the circuit diagram I don’t understand how the main blower relay coil could draw 10 amps and blow fuse 10, even with the AC current from the oscillation. I think the diagram is wrong. I also think that manual temp control for 1996 has no rear blower relay.
Moral of the story is that if you have a buzzing or humming relay, replace it before something fails.