n0v8or

"Automatic mode" functions somewhat different here, but your description is perfectly clear. I used to teach high school (grades 11 and 12) in an American public school. Your written English is superior to most of the students who attended my classes.

Unfortunately, the symptoms of intermittent operation ("blinking"), followed by complete failure, are classic characteristics of LED thermo-mechanical wire bond failure. This type of failure occurs when the fixture designers sacrifice reliability in favor of brightness, or if the LED cooling system (often a miniature fan) fails. There are other possible causes, such as a loose connection or a rodent chewing on the wires, but wire bond failure is more common in high power LEDs than either of those causes.

The wiring and connector may not be accessible without removing the front bumper cover, so there is not many diagnosis actions that are practical. You could try tapping on the failed fog light while it is turned on, to see if there are any short bursts of light output that occur. If the fog light fixture lens is clear, and the LED chip(s) are visible, you might be able to see a black dot on the LED surface where the wire bond fused.