External HDD can be seen in Disk Utility but not in Finder

This fixed mine:

In Finder:
Finder>Preferences>Sidebar>DEVICES>
Then I unchecked and re-checked (deselected and then reselected) "Hard Disks" and they came back. (even though they were external) Basically try unchecking and checking them all.

I'm also now running disk checks.

If the hard drive is showing up in Disk Utilities:

• In Finder click on Go To —> Go To Folder and enter /Volumes
• If your external drive is showing up there drag it to the devices-section in the Finder-sidebar where your other devices (e.g. CD/DVD-drive are)
• You may need to tick external harddrives in Finder settings —> Sidebar before

As I said in a comment above, it seems the “Mount” action silently failed. I assume from the mention of “Tuxera NTFS” in the info on your HDD that you are using that software to get read/write support for NTFS volumes (OS X only offers read support out-of-the-box). The Tuxera NTFS FAQ says:

The most common reason why Tuxera NTFS for Mac doesn’t mount an NTFS volume is that it contains errors or inconsistencies. [...]

To recover from this situation, attach the drive to a Windows computer and run ‘chkdsk /f’ on the drive to repair any problems in its internal structures. See http://support.microsoft.com/kb/315265 for usage information regarding ‘chkdsk’.