Off top of my head, so may not be 100% as I don't use 'side' lights. For clarity, I will use the term daylight running/signature lights, side lights (Tesla occasionally call these parking lights), dipped beam (normal nighttime lights) and main beam (occasional use).
As with ordinary cars, front fog lights can be turned on with side lights, dipped or main beam. Rear fog lights can be used in dipped or main beam. Neither fot lights are active, or rear lights for that matter, with daylight running lights.
However, the car will always revert to auto lights (not auto main beam which is transitioning in its default setting atm) at the start of every drive. So unless you override, the car will control the dipped beam. There are manual settings for side lights and dipped beam but you need to select these at start of every drive, or as you need them, ie driving in fog when it may be bright enough for the car not to recognise you need lights, but you need lights as its foggy.
As a result, if you are in auto mode and you turn on fog lights, the car will I believe turn them off when it thinks it does not need to turn the lights on.
Auto mode also reverts when you get out of the car, so you cannot actually get out and look to see if your fog lights are on if its light as by the time you get to look at them, the car has reverted to auto and turned them off!
Another thing that needs a bit more concentration, is that turning fog lights needs to be done after navigating through a couple of steps on the main screen. So turn them on before you need them in anger - not always possible with the nature of fog. Last time I checked, there was no voice command for fog lights, and even if there was, voice control is not the most reliable if you desperately need it to work.
hth
