Plunger doesn’t stop all water
I'm willing to bet that it is dirt and grime in the plumbing that is preventing a good seal. I would take out the linkage and plunger and clean out the pipe at least to the length of the plunger unit. There are several ways to do this but it should be mechanical in nature, like scrubbing a dirty pan. Here is one example of a tool that you can buy and you can make one yourself with some stiff wire and a rag. DO NOT lose the rag in the pipe!