Do you mean that the hard drive does not appear in the Enhanced Features drawer?
You don't need that, if the hard drive is still mounted on your desktop.
And, if it is NOT mounted, then all you should need to do is unplug (or turn off) the external hard drive.
After saying that, I looked at the What's Keeping Me app some more. It's pretty sensitive to being the active app. I had to click in each area on that app window before something that I want to quit or eject would be available.
And, it looks like the app won't do anything unless there is actually a problem --- that is, an app that won't quit, or a drive that won't unmount/eject.
Try using your Force-quit window by choosing each app to force quit each app, one at a time, until only the Finder is left, then try force-quitting the Finder, too.
Try to eject your disk, until you see an error message that your disk can't be ejected.
Be sure to close that message window, too.
THEN, run the What's Keeping Me app at that time. Should be simple now to see what is truly holding your drive hostage --- maybe.