Looking for information, I did find this:

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But the FAQ has this:

Ignition Switch Replacement in 740/940.
Changing Rear Electrical Part of Switch. [Rick Tilghman/Bill/Jim/Editor] First disconnect the battery negative, then remove the instrument cluster. Disconnect the switch harness connector by pulling straight off the back toward the front of the car. The electrical portion of the switch is just held on with two 3/16 inch slot head screws, the lower of which is difficult to access. A real short 3/16 inch flat blade screwdriver (< one inch) or an offset ratcheting screwdriver is essential since a frame member is in the way. You have to work almost totally by feel because the screws face toward the front of the car. Also essential are a mirror, a lamp or flashlight, and a magnet to retrieve the inevitable dropped screw. Once you get the screws off, just pop the old switch off and the new one on and replace both wire and screws.

The key seems to work- however, turning it backwards a bit experimentally seems to shut things off, and I don't mean taking it to the "off" position all the way, but turning backwards a bit.

Would it be the back part of the ignition switch that is bad or the tumbler part in front I wonder?