So, we fell off the wagon here for a bit. Husband got COVID. He's fine, although he has some residual crap that keeps holding on. Naps nearly every day, taste bugs shot all to hell. But we are grateful. We have been so good in terms of isolation, mask wearing, sanitizing hands, etc. And I didn't get it. Go figure. Anyway, onward, or is that onword?
What’s the problem needing to be solved? There should be two problems. The problem of the whodunnit and the internal demon facing your protagonist. Demon might be too strong a word for, say, a cozy mystery, but your protagonist should have an internal life that either hinders or helps him/her solve the mystery.
In Miss Marple’s case, she is an elderly woman whose biggest physical feat of the day is planting primroses, even though gardening is allegedly prohibited by her doctor due to her many mysterious illnesses. This is an example of a character issue that plays into the Christie plots. To get around this impediment, Miss Marple has minions to move the story forward even though she’s the one who always solves the mystery. Christie’s a plot-based writer (her characters tend to be moribund but she fools us by having ingenious plots), while I’m a character-driven writer (whose plots are ho-hum but I fool you with character studies and a judicious helping of tension).
The best writers are those who have a seamless interface between these two elements. Use your plot mercilessly to move your character development forward. It can be something as simple as your character being afraid of spiders and then having to go into a spider-infested attic to find a clue. Think of Indiana Jones and his thing about snakes. Or a woman in an abusive marriage who is completely downtrodden but does incredibly brave things to prove her fist-wielding husband is guilty of murdering his mistress. Use your plot to make your character face their demons. Remember our Dave Robicheaux? His internal demon is that he’s an alcoholic. Robicheaux’s alcoholism is a major character in all of Burke’s novel.
In cozy mysteries, the demon aspect can be replaced by how the reader relates to your protagonist. Like they’re afraid of the dentist. Or they have a stupid case of eczema on their forehead that no amount of steroids will address so that it looks like you’re walking around with an ever-present case of forehead leprosy. These are issues I face, and if I saw these in a mystery novel, I would identify with the protagonist right off the bat. You should create vulnerability in your villains as well, otherwise they become cliché and cardboard. Vulnerability, relatability, or demons, your characters need depth.