Is there an I without thought?

How do you know that thought cannot end because it is necessary? It is just a belief you have created as trick of your own thought in order to protect itself from an eventual ending.
I do not know if thought cannot end because it is necessary. Is it necessary when you are resting in some place, no working, just having leisure?
My definite response to that question (Can thought end) is: I do not know.

Can you do anything without practical thought?

I cannot, certainly.
If you lay down in your bed fefore sleep… Do you really need thought, while still awake, aware?

It is necessary to think about practical matters whenever one can, so why not prior to falling asleep? If at that time, however, there is no need for practical thought, psychological thought goes on.

When K talked about the ending of thought, he meant psychological thought - not thought, per se - but incoherent thought, specifically.

Agree.
So the valid question is whether psychological thought can end.
I do not know. I keep the question alive.

Yes…