It was pretty easy to see why I had a flat tire. Fortunately, the car was in front of the house and I have a great neighbor who loves working on cars.
First he unscrewed it. You can see the grayish mark of the head of the screw and the hole in the middle. He had a tool to go in the hole and clean it out.
Then he pulls out this sticky rubbery strip - looked like sticky licorice - and threaded it into another tool and applied the glue.
And then he shoved it into the whole. The two ends go up as he pushes down. Then he pulls out the tool and there's just a bit of the two ends sticking out when he's done. He fills the tire and we're back in business.
Good neighbors make life so much better. Thanks Roy.