Anything with properties that can be observed, and which participates in observable phenomena is physical, whether you admit it or not.
To me, non-physical would entail that which is non-corporeal, non-spatial and non-temporal. A great many things fall in this category, including mathematical structures, emotions, pain, expectations to name a few.
Moreover, when I observe the unreasonable effectiveness of math, the geometry, the "lofty structure of all that there is" (as Einstein put it), the existence of successful communication in the universe and in biological systems - I am raptured in the Scriptures which say:
For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, [even] his eternal power and Godhead; so that they are without excuse: - Romans 1:20
This topic doesn't lend its self easily to discussion between persons having different worldviews. We will continue to talk past each other.
I would argue that pain and emotions do not exist independently of the physical body which experiences them.
Ideas are trickier, particularly mathematical ideas that are widely accepted.