The second photo shows the screw I bought at the hardware store, a self-tapping screw made for concrete use. A pack of 3 was about $2.
The third photo shows where to drill a hole. You drill a 3/16 diameter hole through the glove box door and all the way through the hinge. The hole is about 5/8 to 3/4 from the bottom edge of the door. The hole wants to line up side-to-side with the left slot in the hinge (shown with the yellow arrow).
The fourth photo shows the drilling process. You need to reach in the side and hold the hinge in position so it doesn't flip back while you are drilling. Extend the drill bit as far as you can in your drill, you need to drill about 3" deep.
The fifth photo shows a trial installation. The screw cuts thread in the plastic.
It has to be that long to get to the substantive part of the hinge bracket. The washer wants to be big to spread the load over the face of the glove box, since it's soft. But once it's all painted flat black and installed, you really don't notice it unless you're looking for it.
In case anyone's wondering, the use of the concrete screw was not random. I looked throughout the hardware store for a screw with coarse threads that would be suitable for holding securely in plastic, and those were the best I found.
The light works fine. Follow the link in my first post to see how to remove the strut that cushions the door from falling too fast when you open it. Take it apart as that link shows, then either modify like they tell you, or just lubricate the piston as I did. Then after you are done with the fix, reinstall the strut and the light works as it always did.