Explaining self-awareness to non-self aware intelligences

A philosophical zombie is someone who acts exactly as if they are self-aware, but they are in fact not self aware, and the question is, how could you know.

I have a different question.  What if we came upon a new intelligence, let's in this case say it's an alien race.  What if these aliens are INTELLIGENT BUT NOT conscious, and actually KNOW that they are not conscious!  They can talk and write stories and do math and science, but actually, if you ask them if they are self aware, they just look at you funny and ask what you mean, and if you try and explain to them they don't even know what you are talking about.

And how WOULD you explain to them what consciousness means?  You're like, "hey aliens, I know I exist" and they say "what does that even mean?  The brain that is in this body, the one that is speaking to you, contains the information that that thing on the table is a stapler, but this pocket calculator can also contain that information.  The brain in this body contains the information that this brain is a thing in this world, but this pocket calculator can also contain the information that 'this information here is contained in a thing called a calculator which is in a world.'  Heck, a piece of paper can contain information about itself being in the world.  What is special about you that you call this 'self awareness?'"

And I don't know how I would explain to these creatures what I mean when I say that I am self aware.  It seems to me that people tend to assume that if something is intelligent enough to converse with you and have poetry and math and philosophy etc, that it will also have self awareness, or at least that it will SAY that it does.  But what if it does NOT and is actually clearly capable of expressing the fact that it doesn't even know what you mean when you say you have "self awareness" because it has not even had a "simulated" philosophical zombie type of self awareness let alone the real thing?

I like to imagine one of these aliens looking at this blog post and scratching their head.  "What on Zaxar [their planet] is this blog post even about?  This brain in this body cannot even conceive what self consciousness could possibly refer to so what could the fuss even be about."  I have no answer for you here alien.  You'll just have to take my word that there's something out there that I can't explain to you, and I have no idea how it even could work, and you probably think I'm just crazy.