Hi Charlie,

My question is, how do these operate to form the signal for the A11A1U6106 MUX?

The cursor pot itself does nothing special. The wipers are wired to separate MUX input lines. My interpretation is that the processor does the job to find out the direction (and also speed?) of knob rotation based on changes in successive voltage readings.

On start up of the "good" scope I keep seeing this image on the CRT
https://photos.app.goo.gl/GwUdDxu25jh4APwZ6

You noticed perhaps that this is the display shown by ADV Funct -> Cal -> Box -> Run. Normally you would return from this by once more pressing AD Funct. But the scope is stuck and doesn't listen any more to buttons pressed?

Albert