OBERHEIM SYNTH

Interesting problem.  With a scope you could set it to trigger if the supply dips a little,
And see which supply is dipping.  If the dips last long enough, assuming they are dips, then a multimeter may be able to show them as well.  You could recap the supply, but that may not fix the problem.  What if one of the voltage regulators is flaky?  The display uses a separate winding off of the power transformer to create the high voltage that it needs.   Seems like that voltage is dropping out, maybe.  Or some other display issue.  If the cpu voltage was dropping, seems like it might crash, which would look very different.   It wouldnt come right back as it does in your video.   Maybe the 5v analog suppply is dipping?   Best to try to figure out which one, then just fix that one.

Bob