Since you accept as a truism that a material object is that which would exist independent of perception, it should not strain you unduly to conclude that a non-material object is one that does not exist independent of perception.
Well, really the truism part referred to the bit when you said "A non-material thing would be one that isn't material".
Even so,
you still haven't old me what non-material objects are - just what they are not.
You asked for a definition of non-material objects, and received not the one you set forth in quotes above, but a defintiion of a material object is to someone of a materialist outlook no less.
Complaining that you have received nothing but a tautology is false.
Good luck with your inquiry.