A working light bulb does not work, although there is electricity

Hello everyone, at the start I wanted to point out that I searched the forum hoping that I would find a topic similar to mine and thus find out what the problem was, but I did not find it.
Well, I decided to fix the non-working lighting in the bathroom, replaced the cable and after plugging in the bulb, nothing happens.
I started checking the cables for voltage and to my amazement it turned out to be there.
On the drawing I marked the places where I checked the voltage and it is in both.
In addition, I will add that the bulb is operational (I checked it by connecting it to a different power supply).
And my question is what could be wrong that the bulb won't light up.

Greetings.

Have you tried to connect a different light bulb?

Yes, but I wrote that the one I connected is 100% efficient, so it should work anyway.

najdziu wrote:

I started checking the cables for voltage and to my amazement it turned out to be there.

How? A device or a neon lamp? There are no miracles ...

But there is voltage because the "test lamp" is lit, is the voltage CORRECT?

There is voltage because the "tester" is lit, that's just what I checked.

And what is the supply voltage of this bulb or where did you check this bulb?
I suspect that you want to connect a 230V bulb to the 12V network.

so yes: it is a LED MR16 12 V DC bulb (written from the packaging) and I checked it in ... I do not know what to call it correctly, but in the same place on the same ceiling (I have 3 such outputs in the ceiling, in each others everything works fine, just not here).

dedito wrote:

I suspect that you want to connect a 230V bulb to the 12V network.

Yes it can be. The photo clearly shows the transformer from 12V on the secondary.
Measure the voltage at the bulb socket.

If it is a 12VDC LED, it will not be lit because you have the wrong supply voltage.
Yours is 11.8V AC, probably for halogens.

najdziu wrote:

I have 3 such exits in the ceiling, in each other everything works fine, but here it does not).

The question is whether you have the same transformers in these 3 points.

Measure the voltage after connecting the bulb and without a tester because it may distort.

I did not think about it, in fact there may be other transformers in the other two places, and this is a different question now, what kind of light bulb can I connect here? Can you deduce it from this photo?

Halogen 12V connector MR16.
There are probably also LED equivalents, but you need to pay attention to the supply voltage.

What is important has been written.
I close.