***Yes, this is true. 'Thought happens' is a much better definition, although it requires that you provide a definition for 'thought' that may be as shaky as the definition of 'I.'***
You changed the subject here by introducing the term 'definition'. My statement, "Thought happens" was offered as a proposition, not a definition. Of course by using the terms 'thought' and 'happens' I must either assume or provide a definition, or admit that I am using the terms as undefined. Of the three, I guess I am assuming a definition for each term that you would accept.
What I mean to assert by my proposition, "thought happens", is that I know it does from direct experience, and in spite of not knowing anything about what this "I" is that is making the assertion, that "I" cannot possibly doubt that thought happens.
Now, I suspect that that particular assertion would also be held to be true by you. Not because my experience of thought can be experienced by you, or that I can in any way convince you that I experience thought, but because I suspect you have the same kind of experience and that you would identify it by using the term 'thought'. So I think that the upshot would be that we would both agree that "thought happens" although neither of us knows exactly who or what is doing the thinking and perceiving that thought is happening, or how that perception takes place.
***'Something is' is probably the most stable statement of knowledge that I can think of.***
I don't know about more "stable", but I agree it is more fundamental. Your statement asserts only that something exists. My statemet asserts not only that thought exists, but that thought changes. A small step up in information content.