Windows 10: No option to Eject External HARD DRIVE (NOT USB Stick)

1. Click Windows icon in task bar.  Click on Run…
2. Type:

   RunDll32.exe shell32.dll,Control_RunDLL hotplug.dll

3. Press the Enter key or click on “OK”.
4. In the “Safely Remove Hardware” dialog click on the device you want to remove, and press Stop.

(from answers.microsoft.com)

In the resource manager check to see what's using that hard drive. Control Panel/Administrative Tools/Resource Monitor. Or on command line "perfmon.exe /res". perfmon window Go to the Disk tab and see what Processes have Disk Activity on that drive. This won't solve your problem as windows will probably never put in a nice right click, but it may help figure out what's happening and let you do it without shutting down or sleeping.

I found that if you go to Windows/Settings/PC Settings/Devices/Other Devices and click on the name of the device, there is a button to remove device.