I only occasionally use Google Talk, and only via Gmail in my browser. I always stay invisible, and only use it when someone asks me (say, via text or email) to chat with them, and then I send them the first message.
Today I started receiving messages from people, even though it showed me as invisible. I changed it from invisible to available, then back to invisible, and the message "Oops! You are not invisible because you're logged into Google Talk from another client, device, or location that doesn't support invisibility" appeared.
I do not use Google Talk from anywhere else. I use Chrome on various computers, and the Gmail app on my iPhone. I do not have any Google Talk app or anything like that.
The only thing that changed was that I updated the Chrome app on my phone last night, and it looks a bit different now. I cannot find anything about Google Talk in the iPhone Chrome settings.
I have 2-step authentication enabled (and have had it for years). I've signed out of all other locations, changed my password, logged out, and logged back in - and still the problem persists.
What could be making Google think I'm signed into Talk from somewhere else?