"...output of the log amplifier is being
corrupted... possibly by a regular variation in voltage. If the
Advantest uses a switched-mode power supply to create its analog
supplies, there might be a fault in the supply which is causing it to
dither between two different voltages."

If you are right it may be as simple as a filters. I have a tendency to scope the supplies first unless indications are clear that that is not the problem

What we do not see with the still is whether those square type waves are stationary or they move, roll across the display. If they do move and they change direction or velocity with line voltage the answer is right there.

That's the simple answer, if that ain't it then that could be a problem.