Keep integrated screen active when lid is closed

I have a Framework 16 laptop. Sometimes I need to fenagle with the cables behind the laptop. This is easier if I close the laptop. When I close it, Windows (11, but also applies to 10) does not detect the internal screen of the laptop anymore and removes it from the desktop arrangement.
The arrangement with the lid open looks like this:

Screen 1 is the internal screen.
When I close the lid, the arrangement changes like this:

What was screen 1 before is gone now (and the numbers shifted around, but that’s not the point).
Windows is bad at restoring window and desktop icon positions when opening the lid back up again.

How can I prevent the screen from disappearing when I close the lid?

This seems to be a model-specific thing because neither Windows 10 nor 11 act this way if I close the lid of a different laptop.
I also want to clarify that the screen should ideally still turn off while the lid is closed. It should just not disappear as far as Windows is concerned.

This seems like a curious thing to do, but I can see the relevance despite not using a screen.

Unfortunately, I don’t know of any way that this could be done. Unless, perhaps, you were to disable the lid close sensor somehow, maybe that might do it, though perhaps not. I know that on my Framework 13 or other laptops, when I restart the system with my screen closed, and if I’ve gone a step further and removed it from the device manager, it will not show up again until I open my screen. I wonder if some type of physical hardware disconnect might be occurring somewhere, or if it’s just software related.