Of all the possible meanings of the word insightings, here are a few interpretations I feel are most relevant.
insighting
(noun) a blend of
insight
noun
a chance to understand something or learn more about it (Macmillan English Dictionary);
1 : the power or act of seeing into a situation;
2 : the act or result of apprehending the inner nature of things or of seeing intuitively (Merriam-Webster Online)
and
sighting
noun an occasion when you see something, especially something unusual or something you have been looking for (Macmillan English Dictionary)
1 : catching an insight I in some way had apprehended already -> becoming conscious of a previously unconscious notion
2 : deliberately looking into something to understand or learn more about it
3 : attempting to understand my own views by explaining them to someone else
4 : in a very gentle way “inciting” as well -> encouraging or stimulating behavior, especially in myself but also in others (although without the negative connotations)
5 : in-sighting; a form of active introspection that aims at understanding what is going on; ‘apprehending the inner nature’ of my own existence