Man, you made me go out to the garage again. 
You’re right. My Mazda 3 only has OFF, daytime or fog lights or whatever, and ON. I always keep it on ON, so I never even bothered to check after all these years. It’s my wife’s cars that have the AUTO. (Which I keep permanently on ON, as well.) They turn off a wee spell after you turn off your car. I’m pretty sure the 2004 Mazda was the same way, but my memory is obviously not to be trusted. I could find an article about a 2006 Mazda 6 that says this was the case for that model, at least.
My Mazda*, a 2019 MX-5 Miata, does not have automatic lights. But this discussion reminded me of a story. I took my car to the dealer for some sort of maintenance. It was a sort of overcast, drizzly day. When I was in the service department there was a woman there complaining that her automatic lights didn’t come on while she was driving to to the dealership. Every other car on the road had its lights on, therefore there must be something wrong with her automatic lights. I kept my mouth shut, but I was thinking “Maybe everyone else turned their lights on manually. And why didn’t you turn them on manually?” When I did have a car with auto headlights I found that while it reliably turned them on when it was dark, it didn’t usually turn them on in other situations when it would be prudent to have them on, like rain and fog. So I always turned them on manually in those cases.
*There’s seems to be an unusually high concentration of Mazda owners in this thread.
Zoom zoom!
But, yeah, I think there’s way more sense in keeping lights on always and then
dimming them in appropriate conditions (fog) than the other way around. Even in murky daylight conditions, I like the added visibility that headlights afford me. I see little downside to defaulting to headlight always on, but we’re going out of bounds of the thread by now/
I think every car, or almost every car, I’ve had with automatic headlights also turns them on when the wipers are on.
That’s so everybody knows they bought the higher trim level that include fog lamps.
The last car with automatic headlights I owned was a 2009 model. A Corolla, specifically. Maybe newer cars do that, but that car didn’t. I guess I’ve driven newer rental cars with automatic lights, but not in the rain.
All of this behavior is appallingly inconsistent across manufacturers. If you travel and drive a lot of rentals, you’ll be aware of this. Given that many states mandate “wipers=headlights” this one is especially stupid; I’ve noted that if they ever need to balance the state budget, they can just start enforcing this one.
Not necessarily. Those of us who grew up riding motorcycles believe in being visible, and (properly aimed) fog lights help a bit there, presumably.
Not exactly to your point, but … eons ago … during a heavy San Diego rain storm … I had my fogs on.
A guy in a BMW next to me at a stop light held up a little flip sign that read:
“IT’S NOT FOGGY.”
Ayup. Uh-huh. And, technically, he was right 
e.g.,
I’m a member of Candlepower Forums, a group of flashlight and general lighting enthusiasts,and I remember reading a discussion few years ago about using fog lights when it’s not foggy. The general consensus was that it’s not a good idea and here’s why.
At night on a dark road you want to see what’s in the distance so you can take action to avoid animals, road debris etc., right? So if your fog lamps are on they illuminate the road directly in front of your vehicle. Nice and bright…
So your pupil closes slightly because it’s bright, thereby reducing your ability to see far down the road in the light of your main lights.
My memory tells me that some studies were quoted at the time, but I certainly don’t have any references at this time.
Do your own experiment. Go out at night and look into a dark wooded area. Have someone shine a bright light on the ground about 20 feet in front of you. Can you still see as well?
That makes sense–assuming your fog lights aren’t purely decorative, as every OEM set I’ve ever had are. That is, I can’t even tell they’re on unless they’re reflecting off the car bumper in front of me at a light, alas.
And let’s not get into the whole can’t-have-them-on-without-the-headlights thing (different from but related to the question about using them with high beams!).
The vehicles I’ve owned in the last 15 years or so that had fog lamps from the factory were rigged so they couldn’t be on if the high beams were on. Low beams and fog lights, yeah, switch to high beams and the fog laps go out.
Actually, I did this with my truck’s fog lamps. Personally, they added to my ability to see the lines and edges of the road, without using brights. I could see no difference in distance visibility. My particular truck turns* off the fog lamps if you choose brights. They come back on when you dim again.
*Technically should be past tense. Have a new truck now that’s 2 weeks old, with a whopping 114 miles on the odo. It didn’t come with fog lamps, so I’ll have to add them if I want them. Oddly enough, the DRLs are buried in a menu somewhere. Right now they’re defaulting to OFF, but I should probably rummage through the screens again to set them to ON. I’m still trying to figure out why I can’t get the brights to illuminate when the engine is off. This makes no sense to me.