TPMS light remains always off

"I appreciate for any useful ideas" - It could be that the LED light can be broken. If that is the case and it were me in your shoes. I would skip trying to fix the light and not mess with the TPMS on the car and go with a third party TPMS, which are really cheap nowadays (I mean if you really care to know about the TPMS).

Here's one

Here's another one

 

You should be able to tell if the dash light is inoperative - when you first turn the car on it should illuminate all the dash warning lights. If the tire light comes on then you know that it's good.

I remember it taking a while of driving for the system to notice a non-responsive sensor - anywhere from 15 minutes to as much as an hour.
Maybe you just haven't driven it long enough for it to register the lack of signal?

 

Leave your foot off the brake and press the Power button once and release. Then while looking to the right side of the dash light section, press the Power button again and release. All the warning lights illuminate, including the TPMS, but the TPMS is only on for a very brief period. So you have to be ready and looking in the right spot to see it before it goes out.

 

Right, I forgot about that detail.

 

Having the warning light malfunction never come on, could be considered winning the lottery, in some US States where an annual inspection requires functioning TPMS.

 

I was going to ask OP if he forgot to take off the "black tape" someone here suggested to put on with the winter tires. lol

edit: apparently @Mendel Leisk did not advocate this mothod. My bad.

 

Brain bubble? Think I've always advocated the opposite: tape will gum things up, and the light is very low key.

 

Must be! My post edited.