How can a non-working corroded tub plunger with a broken linkage assembly in the open position be fixed?
Yes a coat hanger really helps and on some hard to snag models a bore scope may be helpful.
I have used a long screwdriver to push on a stuck stopper sometimes it’s not corrosion but hair and soap buildup under the stopper that is the problem,
removing the drain will occasionally pull a rat of hair up that is preventing the stopper from dropping into place and blocking the flow.
Make sure to check for obstructions below as the stopper is gravity closure so a chunk of hair could be the problem also.