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You say that this supporting character has little "screen time" but that they are a major motivator in the mind of your primary character. You also say that this character is the cause of a lot of...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/34349 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
You say that this supporting character has little "screen time" but that they are a major motivator in the mind of your primary character. You also say that this character is the cause of a lot of the conflict and participates in the primary character's backstory. So this supporting character is "present" in the mind of the character, through all the struggles and recollections and is hopefully made happy by the ending of the story. A character doesn't need to be physically present, "on-screen" to be important to a tale. Consider the victim in any murder mystery. They rarely have any screen time other than the discovery of their corpse in the opening scene. Still, the story would not even exist if not for their part in it.