Implications of MUXed/MUXless laptops for GPU passthrough

I recently started working on a project which is supposed to automatically analyze to what extend a given system (especially laptops) is compatible with GPU passthrough: https://github.com/T-vK/GPU-pass-through-compatibility-check

I have read that it makes a big difference if the connection between the GPU(s) and the notebook’s screen and dispaly outputs is MUXed or MUX-less:

But I don’t fully understand what the implications of these different schemes are for GPU pass-through.

Assuming we have a laptop with a dedicated GPU, an integrated GPU (which is enabled in the BIOS/UEFI), perfect IOMMU groups and enabled support for IOMMU in the motherboard, chipset, CPU, BIOS/UEFI and kernel:

Would a MUXed scheme mean that the dedicated GPU could be passed between the host and a VM while the integrated one could always be used on host system? And would the host system be able to output on the laptop’s internal screen and external display outputs? And would the VM also be able to do that? Could the host system output on the internal screen while streaming the VM to a window on that screen using looking glass?

And if it was a MUX-less scheme, would that mean that the dedicated GPU could be passed through to a VM and then the VM wouldn’t be able to output to the internal or on external screens?
If that is the case, could looking glass compensate for that problem?

Or would a MUX-less scheme mean, that one the dedicated GPU is passed to a VM, the internal and external displays wouldn’t be connected to the host system anymore and could only be used by the VM?

And is it required to have an external monitor connected in any of these situations in order for looking glass to work?

Are there other important implications?

What are the differences on laptops that have multiple dedicated GPUs. And also laptops that have an integrated GPU as well as two dedicated ones.

When I say MUXed, I am talking about the variant that uses two multiplexers btw (not the one seen o ancient laptops).

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