Q: Cant eject EFI

Might be a corrupt .plist.

Do a backup, preferably 2 backups on 2 separate drives.

Quit the application.

In Finder hold down the option/alt key while selecting the Go menu item. Select Library. Then go to Preferences/com.apple.finder.plist. Move the .plist to your desktop.

Restart the computer, open the application and test. If it works okay, delete the plist from the desktop.

If the application is the same, return the .plist to where you got it from, overwriting the newer ones.

If you want to make your user library permanently visible, run the below command in Applications/Utilities/Terminal.

chflags nohidden ~/Library/

You will need to do that after any updates.

Open Terminal in Applications/Utilities, enter the following and hit Return

diskutil list

You should see EFI as disk0s1. It's the boot loading and formatting partition. You definitely DO NOT want to remove it, eject it or trash it. This is a screenshot from my Mountain Lion. (My drive is partitioned for booting to Snow, Mountain Lion and Mavericks.)

EFI is normally not mounted, but somehow it became mounted. Again in Terminal enter the following and hit Return, which should unmount it. If it doesn't, then I'm not sure what to do next.

diskutil unmount /dev/disk0s1

Alternatively, you should be able to do it this way. Enable the Disk Utility debug menu:

In Terminal, enter and hit Return:

defaults write com.apple.DiskUtility DUDebugMenuEnabled -bool true

Quit and reopen Disk Utility

Then, from the Debug menu, check Show every partition, select disk0s1 and from the menubar, Unmount. (Mount should automatically change to Unmount--if it doesn't, then something else is going on.)

If it's mounted, disk0s1 (EFI) should not show greyed out, as in my screenshot. After being unmounted, it should appear greyed out, the way it should normally appear.

After doing further research, don't think that either of my suggestions will work. Lets try this: Drag the EFI Disk (or whatever it's named) which is currently on the Desktop into Terminal. It should appear as something beginning "/Volumes/..."

Select and copy that, Cmd-C, quit Terminal, re-open and then enter the following

sudo unmount /dev/disk0s1 /Volumes/efi

Important, replace "/Volumes/efi" in the above with what you copied earlier--use Cmd-V. Make certain to preserve the single space between /dev/disk0s1 and /Volumes/efi, or whatever its name was that you copied from Terminal.)

Next, you will be given a scary warning about using sudo. Ignore that and keep going and when prompted, enter your admin password and hit Return. Note, when typed in, you won't see your password in any form, not even as *****.

Wait until you get a new $ prompt in Terminal, which will mean the command finished, then close Terminal. If it responds with some kind of error, please copy and post that here.

If that doesn't work or produces an error, then try

sudo unmount /Volumes/efi

Again, replace "/Volumes/efi" with what you copied earlier when you dragged that disk into Terminal. Make sure to preserve the space.