The vertical bar on this SNES did not bother me too much while I was playing EarthBound.
Then I discovered how much it could be reduced with some additional power filtering.
On this particular console I used two 220 uF, 16 V capacitors and got a very noticeable improvement.
That is the result I observed on this board.
It should not be treated as the only possible SNES vertical-bar fix or as a universal capacitor recipe for every board revision.
The vertical-line symptom is associated with power-supply and filtering behaviour inside the console, and several different approaches have been used to reduce it.
Regrettably, I also discovered what could happen to my EarthBound save while messing around with cartridges.
Fifteen hours of battles and saving…
gone.
Thanks to MaxWar for the help!