There is simple trick to find out Invisible user. The Gmail Chat application that is present on the left pane of the site allows users to appear 'Invisible'  to their contact. For this , You will need the 'Google Talk' desktop application. One you have logged on to your account, follow these steps to determine which of your contacts is invisible :

• Open 'Google Talk' chat application
• Search for contact by typing his/her name in the search box
• Once the name of the contact shows up in the contact list click the entry to open the chat window.

• Click the dropdown arrow present under the close button and click ‘Go off the record’ .

• If you  receive a message saying , “<user ID> @ gmail.com is offline and can’t receive messages right now’  then user is logged off".

• If the above message does not appear after you send a message then user is invisible mode.

This trick is working in most cases so far. However , there may be varying results in case of users who log on to Google talkusing third party tools like mobile chat applications.