Need to shut down to eject external HD.

It is still back to knowing if something is accessing that external drive or not. For instance, I just mounted a random USB stick named STUFF. I opened a Terminal window and changed directory to that external drive. In that Terminal window, I want to see what is accessing that drive and I find the Zsh shell in Terminal and three other processes have a grip on it:

As soon as I change directory out of that external drive, the same command above returns nothing, but it still won't eject… 🤨 even after quitting the Terminal application.

Being UNIX, the operating system keeps an in-use flag with a counter of the application processes (including the Finder) that continue to access a mounted device. When that count reaches zero, then you can eject that device normally. It might be Spotlight indexing; simply having an open Finder window on that mounted device, or a Terminal window.

One of the biggest offenders in my own experience is the Music application. I may have an external drive mounted with a Music folder playing Music. Even after I quit the Apple Music app, I still cannot eject that drive until I reboot. Other times, it ejects normally after quitting Music.

Even quitting the application (e.g. Adobe, Topaz, etc.) that has touched that external drive may not necessarily eliminate any background processes or daemons still running that have that drive in their clutches.