I finally decided that ignoring the problem probably wouldn't make it go away. There was some sagging of the ceiling and plenty of dripping around the duct tape. The tape was giving way, to tell the truth. There was nothing to do but call someone.
I called Cousin Roto, who knows something about inside plumbing. He was the first of the Slumps to have it. We used to go over to his house just to go. I can still picture the line of family members stretching down the hall, some with newspapers under their arm. And I'm thinking, if Roto has a toilet he'll probably supply the paper too.
Well, he was more than happy to come over. He had a saw and cut some holes in the ceiling and pulled it down, fighting through enough black mold to start our own plague. Then it was a matter of putting a patch around the pipe, and it seems to be holding. Thanks, Cousin. For his trouble I put three chickens in his car, which he was happy with.