Many of the craft books I've read on character show what the writer is attempting to define. There's a lot of noise with little substance in many of them, a few special cases but not enough specific generality to provide more than a narrow insight or two. Sometimes things have to be told. I expect writers writing on writing have forgotten how to tell. In my case, I tracked back to first principles after some deep investigation. What is character in literary terms? It is an exponential factor combining all the facets of character.
To some extent physical appearances, which is problematic because outward appearances have little, if any, standard significance to other facets of character and can compromise reader self-identification with viewpoint characters.
More significant are behaviors and personality traits which express character in a meaningful sense. How (supsense factor) will a viewpoint character react (causation) to finding a murder victim (emotional empathy factor)? (Antagonism, all-in-all.) Cynically or traumatically? Or whatever. Behaviors express personality and vice versa. A cynical personality tends to behave outwardly emotionally indifferently. A sensitive personality tends to behave strongly emotionally. An emotional attachment compromised character tends to not care outwardly, but inwardly takes deep offense at un-called for social injustices.
A flat character versus a round character is best when some other facet of a narrative takes priority. Flat characters are auxilliaries in the sense they're secondary to the dramatic action. Kurt Vonnegut's "Harrison Bergeron" doesn't have a single round character. About 4,000 words,
http://www.tnellen.com/cybereng/harrison.html
Another axis of character is static or dynamic. A static character is unchanged by the circumstances of a dramatic action. A dynamic character changes throughout a narrative. The more artful changes are to personality. Though physical changes will do for simple plots where the protagonist pursues resolution of an external main dramatic complication, like prevailing over a nemesis or villain. "Harrison Bergeron" doesn't report any personality or behavior changes, per se, but does report physical changes. It's not a simple plot though. There is an abrupt, profound reversal of circumstances, not so much an abrupt, profound realization of the true circumstances within the narrative's internal world but in readers assuredly.
The above is one of my many diagnostic tools or reading rites for analyzing character and relation to plot. Reading rites become writing rites with practice and application. Another way I procrastinate with good outcomes.
