That's a difficult question to answer, since I must be doing a lot of very different things while thinking. For one, I'm not sure I'm never not thinking. Is thinking different from "brain activity"? We can shut down the model, store it on disk, and boot it back up. Shut down my brain and I'm a goner.
I'm open to saying that the machine is "thinking", but I do think we need more clear language to distinguish between machine thinking and human thinking.
EDIT: I chose the wrong word with "thinking", when I was trying to point out the logical fallacy of anthropomorphizing the machine. It would have been more clear if I had used the word "breathing": When I write I'm breathing, so the machine must also be breathing.