Advaita practitioners believe that we have an eternal self (consciousness) that is one... we can realise the truth.
"one with everything", do you mean one eternal self for every one of us, i.e., we are all one eternal self; if everyone enlightened, i.e., there will only be one thing left, the eternal self? Since not familiar with Advaita concept thus ask for clarification.
Theravadin Buddhists on the other hand believe that there is no 'self'...
Purely a personal opinion, the Theravada School is incomplete, from a Buddhist practitioner's point of view. To remark is, especially if one reading articles on the internet in English about the Theravada School's teaching based on many Pali translated English (modern) Sutras formed the view believed that's what Buddha taught, they could be inaccurate; upto this moment these views and the analogies behind them have a lot to be examined and verified, or even updated.
I just dont see any evidence of anything living on beyond the death of my brain.
One do not die after dead, this the Buddha has used an analogy to make King Prasenajit and others realized the fact:
...佛言。大王。汝見變化遷改不停。悟知汝滅。亦於滅時。知汝身中有不滅耶。波斯匿王
合掌白佛。我實不知。佛言。我今示汝不生滅性。大王。汝年幾時見恒河水。王言。我
生三歲慈母携我。謁耆婆天經過此流。爾時即知是恒河水。佛言。大王。如汝所說。二
十之時衰於十歲。乃至六十日月歲時念念遷變。則汝三歲見此河時。至年十三其水云
何。王言如三歲時宛然無異。乃至于今年六十二亦無有異。佛言汝今自傷髮白面皺。其
面必定皺於童年。則汝今時觀此恒河。與昔童時觀河之見有童耄不。王言不也世尊。佛
言。大王。汝面雖皺而此見精性未曾皺。皺者為變不皺非變。變者受滅彼不變者元無生
滅。云何於中受汝生死。而猶引彼末伽梨等。都言此身死後全滅。王聞是言信知身後捨
生趣生。與諸大眾踊躍歡喜。得未曾有。──《楞嚴經》
It reads as below in English:
...Buddha said, "Maharaja, you see that all are transforming and changing incessantly, thus realized that you would decease. Also during the decease, do you know that in your body there has the not obliterated?"
King Prasenajit holding his hands in prayer replied the Buddha, "I indeed don't know."
Buddha said, "I now show you the no originated-obliterated quality. Maharaja, how old were you when seen the water of River Ganges?"
The King said, "When I was three years old my loving mother took me to visit Deva Jivaka passing by this flow, at that time I have known it was the water of River Ganges."
Buddha said, "Now you are lamenting your gray hair wrinkled face, the face must be more wrinkled than at childhood. That by now you observe this River Ganges, as in the past as a child observing the river this seeing has the difference of young or aged not?"
The King said "No, World-honoured One."
Buddha said "Maharaja, although your face wrinkled yet this essence of seeing has never wrinkled. The wrinkled is change, the not wrinkled not change; the change is to be obliterated, that the unchanged essentially is not originated and obliterated, how so in it do render to your living or dead? Whilst still quoted those such as Makkhali [Gosāla], and said the same that after this body died all annihilated?"
The King heard this, truly knew that deceased yet living after the body. With the rest of all rejoicing in jubilation, obtained the never have had before.
The above is quoted from the Surangama Sutra translated into English, by me :]. Surangama Sutra has been disparaged by many, both in the Chinese language source and others. Here I will bypass to tangle in examining its authenticity. IMO it's the Buddha's Sutra as solid as the rest. It's said that this is the 1st Sutra to disappear at the ending of Dharma time; the last is the mantra "Namo Amitabha". If you read this conversation between King Prasenajit and Buddha, you will get that there is the essence (of you) that will never die, as King Prasenajit. I got it when reading this part. Since I'd known the non-dying in me in other experience, I was not as exhilarated as the King and others, only slightly gladdened. Hopefully it works for you, and brings about the same effect ;). Else try to contemplate few more times to get it.
...the concept of Annatta... what is it that is reborn? ...Nothing is observing something?...
Wow, I'll leave this to later maybe, since my answer is so long now, and not sure if I could produce an accurate answer... I'm reading the Mahāparinirvāṇa Sūtra and Laṅkāvatāra Sūtra, hopefully I could come up with some more "prajna" to answer your question ;].
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*Below is my own exercise, for the convenient of writing, just disregard.*
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...佛言。大王。汝見變化遷改不停。悟知汝滅。亦於滅時。知汝身中有不滅耶。
- ...Buddha said, Maharaja, you see that all are transforming and changing incessantly, thus realized that you would decease. Also during the decease, do you know that in your body there has the not obliterated?
波斯匿王合掌白佛。我實不知。
- King Prasenajit holding his hands in prayer replied the Buddha, "I indeed don't know."
佛言。我今示汝不生滅性。大王。汝年幾時見恒河水。
- Buddha said, "I now show you the no originated-obliterated quality. Maharaja, how old were you when seen the water of River Ganges?"
王言。我生三歲慈母携我。謁耆婆天經過此流。爾時即知是恒河水。。
- The King said, "When I was three years old my loving mother took me to visit Deva Jivaka passing by this flow, at that time I have known it was the water of River Ganges."
佛言。大王。如汝所說。二十之時衰於十歲。乃至六十日月歲時念念遷變。則汝三歲見此河時。至年十三其水云何。
- Buddha said, "Maharaja, as you said, during twenty was weaker than at ten years old, nonetheless at sixty; days, months, hours and moment by moment that's changing. That when you were three-year-old seeing this river, up unto at thirteen how so the water?"
王言如三歲時宛然無異。乃至于今年六十二亦無有異。
- The King said, "Clearly has no difference as at three years old. Even by now at sixty-two there has no difference."
佛言汝今自傷髮白面皺。其面必定皺於童年。則汝今時觀此恒河。與昔童時觀河之見有童耄不。
- Buddha said, "Now you are lamenting your gray hair wrinkled face, the face must be more wrinkled than at childhood. That by now you observe this River Ganges, as in the past as a child observing the river this seeing has the difference of young or aged not?"
王言不也世尊。
- The King said "No, World-honoured One."
佛言。大王。汝面雖皺而此見精性未曾皺。皺者為變不皺非變。變者受滅彼不變者元無生滅。云何於中受汝生死。而猶引彼末伽梨等。都言此身死後全滅。
- Buddha said "Maharaja, although your face wrinkled yet this essence of seeing has never wrinkled. The wrinkled is change, the not wrinkled not change; the change is to be obliterated, that the unchanged essentially is not originated and obliterated, how so in it do render to your living or dead? Whilst still quoted those such as Makkhali [Gosāla], and said the same that after this body died all annihilated?"
王聞是言信知身後捨生趣生。與諸大眾踊躍歡喜。得未曾有。
- The King heard this, truly knew that deceased yet living after the body. With the rest of all rejoicing in jubilation, obtained the never have had before."