No linkage available . I did spray bleach down in the overflow and down the drain and just let it sit overnight then ran water. So far it seems to have helped.Interesting. With the drain open, maybe the overflow riser acts like a chimney allowing flow, and closing the drain stops that air flow.
Did you try spraying bleach solution into the overflow, and have it spread around inside as well as you can?
Have you pulled the linkage out of the overflow and cleaned?
There are two common types if you have a trip lever.
I’m going to continue to do it once a week for a bit.