BMW e46 Rear Fog Light Issue: Car Icon, Relay, Fuse - Troubleshooting and Solutions Needed

I can't come to an agreement with my car.

The rear fog light does not work and the large car icon is still lit on the meter. There is no typical notification of burnt light bulbs in my car, in return the supposedly burning car icon is responsible for it. And that is causing me a lot of problems now.

What is important is that by turning on the fog light button, the indicator light responsible for this information lights up, but I do not hear any sound of the relay.
In the case of front fog lamps, I can hear the sound of the relay.

The first question is whether this rear light is also turned on by a relay and if so, where to look for it?
The second question is which fuse is responsible for this light?

First of all, LCM, secondly, when you start repairing, at least the description of the fuses.
We do not support laziness.

pp the first is a few versions of the fuse lists.
to the extent that I started to translate this list on foot, but it takes quite a long time and I do not have time for it today, so the accusations are sorry but very unfounded because I am the first to criticize others for laziness on the Internet. The question about safety asked because, or maybe someone else will surprise me with something.
Secondly, the logic of how the indicator on the counter works, it should not work in the event of a faulty fuse, because it would be misleading and the driver would not be aware that there is no light.
Thirdly, by connecting the computer to the car, there is no reported error of this light failure.

Fuse 38 in the glove box.

For me (pre-lift station wagon) there is one bulb, the other side is a dummy, the rear anti-fog relay cannot be heard (the front one is audible) in the driver's seat. Did you check if the bulb is burnt? If the car icon is on, have you checked what is communicating to you?