OK, let's forget the philosophy for the moment, I'm not particularly interested in Ramachandran's metaphysical leanings.
If self awareness can be measured in some sort of experiment
What we are talking about when we say "consciousness" or "awareness" is the very fact that we are aware of anything at all. "Self-awareness" is one step beyond that, and it means "aware that I am aware" or "aware that I am separate from everything else." But judging by the rest of your post...
(drawing on monkey faces or whatever..) and we suspect that mirror neurons enable this, then an experiment can be performed to demonstrate whether or not self awareness can be reduced to the function of mirror neurons.
I can't see the scientific problem here.
...you are now talking about self-recognition of the physical body
. You are talking about a system which is analysing sensory data, and processing it, working out that physical object it is sensing corresponds to "itself". Now...monkeys and dogs seem to be able to do things like this. Siamese fighting fish are totally incapable of it, and will relentlessly attack a mirror placed in their tank.
There's two aspects to this. The first has something to do with pattern-recognition. It has to to do with the ability to process the data coming in. There is no scientific problem explaining this ability, because it is typical of the sort of things brains do all the time. I can also imagine it is possible for a robot which is not conscious to learn how to recognise it's own "body" by trying to match up the instructions it is giving to its mobile parts with changes in the sensory data it is recieving.
The robot isn't conscious, but it is capable of doing the thing you claim is evidence of "self-awareness." Do you see the problem? There's no scientific difficulty in carrying out this sort of experiment, but it doesn't lead to any progress towards solving the Hard Problem. It doesn't close the explanatory gap, even if it might tell us something interesting about the way brains work.