As the fall approaches, darkness descends and I notice the headlights in my rearview mirror more. How does that anti-glare switch work anyway?

Except for the one Alice stepped through, most mirrors have a thin shiny layer of metal that does the reflecting, with a sheet of glass in front for structure and protection. The interior rearview mirror of most cars has an ingenious variation, in which the surface of the glass is not parallel to the mirror at the back. It is a wedge. The Guide Lamp division of General Motors worked on head and signal lights and also came up with this solution to headlight glare in the early 50s.

Although glass allows light to pass through, some of it is always reflected but you only see this when it's darker in the surroundings. The front glass surface of the rearview mirror reflects only about four percent of incoming light.

In the day time, the silvered back of the rearview mirror reflects the scene behind you and some reflects off the glass front and away. The front glass also reflects a faint image of your lap but because the main image is so bright, you usually won't notice it, unless your pants are on fire.

At night time, your pupils dilate so you're more sensitive to light levels. By flipping the tab, you change the angle of the mirror so that the headlights bounce off the silvered surface and away from your eyes, while a small amount bounces off the front surface of the glass so you can see a dim image of the headlights.

I couldn't find the exact angles involved in making these mirrors and maybe some refraction might also play a role in the angles but I think this is the general idea. And you should be able to make it work in either position by adjusting the mirror, except that it bounces off in a different direction. If you have a flashlight, you can test out these different sources of reflection. Just don't do it while you're driving please.