Discussion about the Korg PolySix synthesizer

If it's the same pattern every 8 notes I'd suspect interference from the
key assigner.
I believe Dan Backshall already suggested checking the keyboard cable.

The key assigner is located on the voice board so it "leaking" into the
voices is a possibility.

Several wild guesses (again):
The noise volume clearly was modulated by the LFO hence it must be injected
somewhere before that part (VCA modulation happens on the effects board).
The difference in noise volume could be the result of different attenuator
settings; please check this. The attenuator circuitry is also on the
effects board.
You could check the signal directly at the voice board output and see if
there's  already noise.

I seem to recall that there actually was a field modification to keep the
keyboard cable away from the other boards because it would interfere. The
keyboard cable is fastened to the frame in two locations (with a clip and
with a wire); if one of them went missing it could result in some strange
behaviour.
You could try to remove the keyboard and check if the noise changes if you
move it a couple of inches away (while still being connected).

There could also be a problem with the effects board. Depending on the
damage to the processor board (and how the Polysix was stored) the damage
could have spread to the effects board right next to the battery. I have
seen several acid-damaged effects boards.