My lavatory pop ups do not work. Looking down the drain there doesn't seem hardly anything left of the pivot rod tip that goes under the pop up plug. Do the tips of pivot rods corrode away? This is a VERY old house.
If I have to replace them, are pivot rods standardized? Do they have the same threads on the retaining nut, and the same washers and gaskets? Again this is plumbing from a house built just after WW 2.
The thing to do is to get a new pop-up rod assembly and try it on your existing drain.
If it doesn't work, replace the drain and tailpiece with the kind with a pop-up assembly.
Just unscrew the old drain to remove it. You might need to heat it up with a hair dryer to soften the old plumber's putty first.
Clean off the old putty, roll a roll of fresh plumber's putty in your hands, wrap it around the sink drain hole under the new drain lip, tighten the drain down and wipe off the excess putty.