If you think that someone is invisible on Google Talk and not actually offline, then you can catch that person easily. To detect if a person is invisible or actually offline on GTalk, follow this procedure:
• Sign into your Google Chat either via Google Talk or via Gmail.
• Next open the chat window with the user you want to check on.
• Go to options and click on “Go off the record” as shown below. For users who have signed in via Gmail click on “Videos & more” on the bottom left of the chat window and then choose to “Go off the record”.
• Now send any message to the user.
• Here by, if you get an error message in red font, “<username>@gmail.com is offline and can’t receive messages right now”, then the user is really offline.
• But if you do not get any such message then it means that the user is not offline but is in invisible mode and you have caught him/her.
The only catch in this is that, you can put the chats off the records when that person is online, so you must see hime online on GTalk at least once to use this method.