By most interpretations I have heard and have been taught, it is most definitely an internal characteristic. I think you will need to go pretty far to find a source that doesn't agree with the concept of neshama- the uniquely Jewish soul.
What’s the earliest source you have for this soul of which you speak. And don’t cite Bereshis because that can simply be taken to mean a spirit of life, so I’m asking for sources that can’t be taken to mean that, and are specifically referring to such a Jewish soul.
/Devils advocate