Apparently you misunderstood. I said the thinker
is thinking, not the thinker is thinking.

I.e. the action and the object are the identical phenomena. There is no difference between the 'object' and the 'action', which IMO means that there is not actually an object, but in deed only the action or in this case perhaps a better phrase is the phenomena.
It is true that usually where is action there always is an object - in the physical world.
A river flows. Rain falls.
If for some reason the flow of the river should stop, the river would still be there, it just would not move anymore. Likewise, if the rain should for some reason cease to fall in mid-air, there will still be rain. It just simply ceased falling down. So the action and the object seem to describe different things. The object is the matter as such (water the river consists of / water the rain consist of) and the action is how the object changes in relation to its exterior (change of position within space).
Now what happens when thought ceases. Is there still a thinker?
And what does the thinker consist of, since it can not be thought itself if that is only something the thinker does.