I don't have any issues with TK: The Eye. You can try deleting the loggerhead.lua file from your savedvariables directory and see if that helps. Keep in mind that doing so will reset all of your preferences.
In the LoggerHead configuration, it lists one of the Outland instances as "The Eye". This is incorrect. There is no instance that is specifically called "The Eye". When the command GetRealZoneText() is used, it returns the name of the instance as "Tempest Keep". That's why checking "The Eye" as an instance you want LoggerHead to enable combat logging for, doesn't work. Because it's looking for an instance called "The Eye", when the name of the instance is actually "Tempest Keep".
This is further confirmed if you enable "Prompt on new zone?". When you turn this on and enter Tempest Keep: The Eye, it says "You have entered Tempest Keep. Do you want to enable logging etc..." It doesn't say anything about "The Eye".
Again, this is even further confirmed, when you are in "Tempest Keep: The Eye" and do the command "/who <myplayername>" it will list you as being in "Tempest Keep". Not "The Eye" or "Tempest Keep: The Eye".
And continuing, if you look in the LoggerHead config again, under "Zones > Outland" it lists "Tempest Keep" there. Tempest keep isn't really a zone, its an instance. I mean all instances are zones, but they are really better described as instances. If you 'check' "Zones > Outland > Tempest Keep" THEN LoggerHead will work with TK The Eye correctly. It's just in the wrong place in the LoggerHead configuation.
The correct fix for LoggerHead would be this:
1. Remove "The Eye" from "Instances > Outland"
2. Move "Tempest Keep" from "Zones > Outland" to "Instances > Outland"
In the meantime, the short term fix for this is to simply enable combat logging for "Zones > Outland > Tempest Keep". It doesn't matter if "Instances > Outland > The Eye" is checked or not.
This will fix the problem and make sure people are not confused by this anymore.