Non duality and eternal life

I have no idea how would one be able to prove that. Near death on the other hand can be researched scientifically. And even research in that area can be sketchy, depends of course on the research method and so on.

Anyway. If you find NDE acceptable as proof of existence beyond death, then I could advise books by Pim van Lommel. A Dutch cardiologist who did a few studies.

See:

• https://www.iands.org/research/nde-research/important-research-articles/464-dutch-nde-study-attracts-worldwide-attention.html
• https://www.amazon.com/Consciousness-Beyond-Life-Near-Death-Experience/dp/0061777269

Hope it helps.

The Mulapariyaya Sutta deals extensively with questions of "our self awareness".

Perceiving earth as earth, he conceives [things] about earth, he conceives [things] in earth, he conceives [things] coming out of earth, he conceives earth as 'mine,' he delights in earth. Why is that? Because he has not comprehended it, I tell you.

The sutta goes on to describe an alternate perspective:

Directly knowing earth as earth, let him not conceive things about earth, let him not conceive things in earth, let him not conceive things coming out of earth, let him not conceive earth as 'mine,' let him not delight in earth. Why is that? So that he may comprehend it, I tell you.

That perspective is extended to assert:

Because he has known that delight is the root of suffering & stress, that from coming-into-being there is birth, and that for what has come into being there is aging & death. Therefore, with the total ending, fading away, cessation, letting go, relinquishment of craving, the Tathagata has totally awakened to the unexcelled right self-awakening, I tell you.

In other words, the sutta invites us to consider such questions through the evidence of our own practice.

I'm not sure how much emphasis you place on the "self" in self-awareness. I'm also not sure what you think of as "hard evidence." However, I do think it is possible to arrive at the conclusion that mere awareness cannot be extinguished with the break up of the body through pure reason alone. Is this what you are interested in?

It was reading about various people’s experiences of recalling previous lives and experiencing consciousness outside of the body that helped me to shake my materialistic world-view. Some of the descriptions are so convincing. It was the motivating factor that made me try to get establish how consciousness could arise from purely physical sources, such as exist in our brain. I used a thought-experiment where I compared our brain to a computer and tried to establish how my direct experiences such as creative reasoning could arise from a combination of hardware and software. Certain scientists claim that artificial intelligence is possible that can directly mimic the functions of the mind, but they are just claims. AI can appear to be very clever, but it always requires human programming and interpretation.

I know there is absolutely no concrete evidence of reincarnation. I'm not denying its possible.

First, you need to understand what is an Empirical evidance, with that, you have to understand that in the matter of the object of your question, an empirical evidence based on pure observation cannot be provided, no matter what.

The accounts of rebirths are purely subjective if you google about such matters, you will find that some authentic psychologists have indeed written books based on tons of interviews they have conducted. Now as a direct evidence cannot be obtained and all the data collected is subjective, all this research goes down the drain as 'pseudoscience' or worst 'woo-woo'.

So when you say the concrete evidence is not present, the problem is concrete evidence cannot be given in the first place. On similar lines even, 'human consciousness' has no concrete evidence, the only way I know you are conscious is because I am conscious and based on your activity and my experience I can only infer that you are conscious. This has led few scientists to say that consciousness itself is an illusion. So lack of empirical evidence doesn't imply the non-existence of something.

the self-aware part of the us-the part that's aware we are thinking goes beyond death and was here before birth?

This is again the Hindu theory of eternal Aatman, but in the Buddhist context, the Buddha said in Assu Sutta,

This is the greater: the tears you have shed while transmigrating & wandering this long, long time — crying & weeping from being joined with what is displeasing, being separated from what is pleasing — not the water in the four great oceans.

So, he clearly indicated that part of you goes on living even after death, but where the Buddha contradicts with the Hindus is that He insisted that the self itself is an illusion, so what lives of you after the bodily death is an interplay of five aggregates, the exact dynamics has not been mentioned.

Is there any hard evidence for this ?

I will tell you a small exercise, do it for yourself, you will get a hard subjective experience.

1. Lie down and relax on your back, be completely relaxed, now try to remember the memories early on your life as possible, do this for 2-3 days.
2. Next, try to remember and focus the memories of your life between 3-4 years of age, this is the time you would have just started feeling the sense of 'I', sense of separateness.
3. Now focus on all the memories where you are in action, where you are doing something, there will be memories where you will be motivated to do something unusual, there will be memories of you doing things instinctively which have not come from your parents or siblings or from TV or from any source possibly there. These are instincts you have followed from past lives. Mant things in our current life, we go on doing in oblivion.

Now, this is not a hard empirical evidence, it's solely your own worldview out of your own experience. There is an obvious ability of human mind to know things. Skeptics are mere Physicalists.