Hi Spencer,
Please use a button element instead to make it clickable. Text option of the button element can be disabled, then enable the graphic option to use ICON. Then set the link on LINK OPTION.
Displaying different button for logged in or log out user though is not available on the theme. You might need to use a third party plugin or a custom development. Unfortunately, this is outside the scope of our support. Thank you for understanding.
In case I misunderstand your issue when you say it is not functional, please give us more information so we can help you better. Thank you.