To me, self-realization is discovering your essential self - a presence beyond your life story. This often presents initially as an unbiased observer or witness - like the background to all experience. After the "witness" is known and given enough attention, suffering begins to wane and a general peace and stillness pervades. In this initial phase, Consciousness is often experienced as looking through our eyes and may be recognized as the same presence that looks through the eyes of others - this is often the first recognition of oneness.
When this initial phase of self-realization begins to "settle" or integrate, we often experience Consciousness "closing the gap" between the background and foreground. It's often as if Consciousness is discovered initially in the background of our perceptions - at the source of our looking, sensing, or perceiving. This is true, however an identification with the body almost always remains for awhile after self-realization and so it seems as though Consciousness lives in the body or is "located" behind the eyes or in the background somehow.
When self-realization begins to integrate we notice that it is not in the background and an interest in the true nature of experience may begin to stir. This is what I call the spiritual-awakening process. In my work, self-realization is often the first step in spiritual awakening. After we realize our true nature - as a changeless presence - we can begin to explore it's unbounded, eternal, infinite, and loving nature. When we know our nonduality, experience becomes a vehicle and invitation to explore the true nature of life and integrate this wisdom.
Traditionally, people may isolate and protect the sacred wisdom revealed in self-realization - for example by sitting in a cave. It may be important to enter a phase of reduced stimuli and responsibility while this initial divine understanding is "settling". But moving outward and allowing the full experience of being a human allows nondual wisdom to penetrate the heart and gut - which are distinct forms of enlightenment. To me, this is the emergent expression of nondual awakening - no longer reserved for the reclusive lifestyle. So that the "messiness" of life is experienced as sacred and actually deepens the awakening and literally illuminates the mind and body.