Why is the boot sequence no more visible with a Gainward GTX 1060 Phoenix?

It appears that solving this issue is not possible without manufacturer help (unlikely, Gainward is a low-cost manufacturer from what I understand).

In this answer it appears that the graphic card could either duplicate the output on all ports until the drivers are loaded, or output only to "port 1", which in my case appears to be HDMI. My card does not have a setting to change the behaviour and it does not detect whether Port 1 actually has a monitor connected.

Which screen gets BIOS output during the boot process is up to the graphics card. Some graphics cards output to all displays simultaneously, some will only output to whichever port it considers to be "port 1". Most of the time they're not labeled. In the case of multiple graphics cards, the display goes to whichever one the BIOS detects first. Some BIOSes have a setting that lets you determine if an onboard vs. discrete card should be treated as the "primary".

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Also... some BIOSes do not detect whether or not a screen is attached to the primary display and some do. In the cases where it does, "port 1" might change depending on whether the TV is on or set to the right input. In cases where it doesn't, output may go to the HDMI port whether there's anything connected to it or not, and you may not see anything on either screen.