I was able to start the engine. Last night, I noticed that, when reinstalling the switch, the key-in-lock warning chime only comes on when the switch is tight against the lock housing.

So, this morning, I checked and, sure enough, if you put the key in the ignition, and turn the switch with a screwdriver, if you press down in the slot with the screwdriver while turning, the car will start. Fortunately, it continues to run after you release the downward pressure. I guess this is an additional anti-theft measure. It was not necessary to have the key in any particular position. It just needed to be inside the immobilizer ring.

It looks like the steering wheel needs to be removed to get the switch out? And even then, it looks like the whole steering column has to come out to get access to drill out the shear bolts?

PS. The failure seems to related to the steering wheel lock mechanism. Engagement of the key mechanism vs failure to engage can be made to come and go by locking the steering wheel and wiggling the wheel back and forth while pushing in on the key.