External Hard Drive Won't Mount on my 2018 MacBook Pro
Short Answer:
I removed the HDMI Cables from the Thunderbolt ports and connected the 8TB external HD in isolation and it was then recognized and worked correctly.
Longer Answer:
After doing some basic diagnostics failed to yield any clues, I had an epiphany: I was now using dual HDMI monitors connected to my Thunderbolt ports- (1) HDMI cable connected into a Thunderbolt port on each side of my 2018 MacBook. Generally, I don't use these.  Was it affecting the power is some undefined way?
So I unplugged the monitors and just plugged the 8 TB external hard drive into a Thunderbolt port by itself. Bingo: it was recognized and sprang to life. Of course you can plug the MacBook's power cable into any free Thunderbolt port while the External drive is connected as the power cable is definitely going to be power-in and not drawing power FROM the MacBook.
To validate my understanding, I used a USB-C pass-through power meter and plugged the external HD into it. The arrow in the below picture revealed that although the external HD had its' own external power supply/brick, unbeknownst to me it was nonetheless drawing power FROM the MacBook. So with the HDMI cable connected to the other Thunderbolt port on the same side of the case, it appears that affected the available power to the external hard drive.
Although this solution deals with an external hard drive, I'd suggest when troubleshooting any device connected to the Thunderbolt ports which is presenting with issues to connect the device in isolation- unplug all other devices- while testing it.
Hope I saved somebody else from needlessly buying a replacement external hard drive!