Racerman27410's post appears to be correct. When I took off the hardtop again I could see space around the "plug." I was quite excited by this. So I got out some RTV silicone and pushed the nozzle of the silicone's tube in and around the "plug." I wish I had read Racerman27410 's post better and realized I was supposed to take the "plug" out, fill the hole with silicone, and then put the "plug" back. Anyway I thought I was just supposed to push the silicone in around the "plug."
I let the car sit for about 20 hours or so to cure the silicone before I dumped a 3 quart saucepan full of water on the area. No leak. At this point I was cautiously optimistic, but...
Later I took the car outside and gave the driver side a good hose soaking and water started coming in the driver's side. (I gave it quite a long extended soaking however.) Maybe in most rain storms it will be OK.
A long soaking on the passenger's side did not result in any leaking.
I am somewhat mechanical, but no where near like the others on this forum. Maybe I should have taken it to a dealer. I guess I still could. Maybe I'll just see how bad it is in a rain storm. And I guess I could always hope when I start using the soft top that the problem will go away.