"How exactly does an artwork give an insight into an artist's mind?"
An artist’s work is a spark of his/her insight.
Now when I look at other’s work, it is like looking at the visual representation of another mind. I immerse myself with it and enjoy details or marvel the unexpected or the least concept I would have thought of. Then I ask: “What’s in his/her mind when this work is being done?”
In my site, I mentioned the circumstances, people, concepts, and even plain words that has driven me to do my art. And why will I not say so? Appreciating art is the same as being driven by inspiration. I consider that a special social experience, there is no need to be arrogant or ill-spirited about it, unless it is private to elaborate. And when it comes to art, my threshold to inspiration is sensitive and easily ignited.
The work of others and tons of things only inspire me. I look for surprises and ticks. I start from there.
Hope I was able to answer the question.