The confusing part about "proving existence"

I'm trying to follow the idea of "proving I exist" from various meditation books I've read—Spectrum of Ecstasy, Spacious Passion, Rays of the Sun, The Myth of Freedom, and the opening chapters of Seeing That Frees.

The idea is that we experience attraction, aversion, or indifference to whatever we experience depending (only? mainly?) on whether that experience supports or undermines the case for our existing, or is neutral. We want to prove that we exist.

For example, if someone pays attention to us that might be attractive, because they're acting as if we exist and therefore reinforcing our sense that we exist. On the other hand, if they act as if we're not here, that might be aversive because they are behaving as though we don't exist—in a sense weakening the case that we do exist. (In what sense?)

We call these things that evidence our existence "reference points." The things that undermine the case for our existing might also count as "reference points"—I don't recall.

The previous example is straightforward, but other examples I've read are not so clearly about existing, in the most baisc sense.

One category of such examples is about identity. If I think that "I am a clever person" and then I do something I realize is foolish then that undermines the case for my being a clever person.

Now here's the part that confuses me: "Being a clever person" is using a different sense of being than existing. If "I" want to prove that "I" exist, how does it help "me" to prove that this "I" has the property of being clever? Such a proof doesn't seem to substantiate the connection between "I" and experience. Isn't that what we'd need to do? It seems this proving a property of "I" stuff only smuggles in the assumption of existence by way of an assumption that if "I" am a certain way then "I" must exist.

But what would it even mean to prove a connection between between "I" and experience? I suspect this goes back to the joke at the center of opening awareness: When do we get little proof of existence thingies? We don't.

I wonder how things would have to be for such a proof to be possible. That could explain why the answer is "we don't."