Windows 10 does not give me the option to eject external hard drives

It may not be a problem. Have a look at your disk drive in Device Manager, in Properties/Policies.

If Quick removal is set you don't have a problem; your data is not at risk.

[Answering for anyone else who finds themself here, like me, and wondering the same thing!!]

I don't have a policies tab displayed; any suggestions

If your tabs include the others but they are missing the Policies tab, look at bottom left of the pop-up and click on Change Settings. The policies tab will then appear.

And for others, to get to this particular Properties pop-up window, you need to right-click over your portable hard drive name in file manager, select Properties. Then select the Hardware tab. Find the name of your portable hard drive in the Hardware list, highlight it, and click on Properties at bottom right of the pop-up.

[Answering for anyone else who finds themself here, like me, and wondering the same thing!!]

I don't have a policies tab displayed; any suggestions

If your tabs include the others but they are missing the Policies tab, look at bottom left of the pop-up and click on Change Settings. The policies tab will then appear.

And for others, to get to this particular Properties pop-up window, you need to right-click over your portable hard drive name in file manager, select Properties. Then select the Hardware tab. Find the name of your portable hard drive in the Hardware list, highlight it, and click on Properties at bottom right of the pop-up.

Right click the Windows icon in task bar on the far left.  Click on Run…, and type in:

RunDll32.exe shell32.dll,Control_RunDLL hotplug.dll

Press OK.

That will bring up the “Safely Remove Hardware” dialog.

From this dialog you can click on the device you want to remove, and press Stop. Once Windows is done with it, you are told you can remove the device.