The drive, that has been cruelly rejected by my Plex box, works perfectly as a SATA attached drive in my main desktop PC. It also works perfectly as a USB attached drive in the Plex box. It's brother, an identical (or so I thought) Toshiba x300 8TB, works perfectly in any socket on the Plex box, and any cable.
I've heard of motherboard drive controllers and channels going wrong, but I've never heard of them developing a grudge against a particular device.
If I can't find anything to fix it, I shall attach it as an internal USB 3 device with one of
these, or similar. I can snip the power cable and attach it to the 12V & GND pins from a Molex. That
way it will reboot with the rest of the drives.
Probably get it finished just in time for the motherboard to fail altogether.