I am sorry you are having problems with the system but let me help you.
Please note that I have tested the same model from my side with a direct HDMI connection and it is working just fine. As you mentioned before, the issue seems to be caused by the adapter you are using. I would recommend you testing another passive adapter (better quality) or active adapter.
There's just as much possibility it's the NUC as it is the adapter.
Obviously I've asked the product vendor to investigate but I suspect they will give the same comment as you and blame the NUC.
I don't understand what you mean by testing another adapter, are you recommending I buy another adapter and try it.
AFAICS there aren't any other external CEC adapters that suit my needs.
But since you have replied with the expected response perhaps you can help by providing information on BIOS settings that may help.
I can't remember now but does the NUC BIOS provide the ability to specify a custom EDID and if so will that cause the HDMI video signal to be provided regardless of what is or is not connected?
We do not recommend using adapters. We do recommend using direct connection but if you have the possibility to test a different adapter it depends on you.
In regards the option to specify a custom EIDI at this point is not available at the BIOS level you can just select different devices to boot but the signal will be with the features the output port have.
I have the same adapter and had the same issue. You can solve it temporarily by connecting the adapter to a USB 2.0 hub, then connect the hub to the NUC.
Then, update your BIOS to the newest version (0030 as of now) and enable the "Deep S4/S5" option in the "Power" menu of the BIOS. This will solve this issue and other USB 3.0 issues that the NUC has, like USB 3.0 drives not being detected after a cold boot. From then on, you will no longer need the USB 2.0 hub and the adapter will work just fine, connected directly to a USB 3.0 port on the NUC.