I'm quite interested to read your responses to this question. My take is that thoughts merely arise in consciousness. Thoughts are not chosen. They appear. Prior causes impact what appears but no thinker thinks them. The idea of thinker is another thought that appears.
Read the book I Am a Strange Loop sometime. It makes a convincing case for consciousness merely being a background "observer" process. This is the way I tend to think of it. I suppose it appeals to me as a software developer.
In other words it is not so much that we are thinking and are therefore a thinker, as that we're observing and responding to those observations. Our observations are often wrong or incomplete, and our responses are often poorly considered or outright irrational, and our thinking is frequently disordered. But we tend to get used to being the observer and influencer and having feelings about it and goals around it and so forth.
So no, I don't think there's a thinker in the way most people think there is, but I don't think that thoughts "arise" out of some ether, either.
There is a thinker, in the sense that there is a human brain in which these thoughts are occurring. I think it's true that thoughts are not chosen, and just appear, and that prior causes impact what appears. But they are still in your physical brain.
The thinker might be the cosmos or Ultimate Reality.