For me, a cozy is pretty light, as you say. Poirot is NOT Cozy; Miss Marple is sometimes. The actual 'kill' is never described. Tommy and Tuppence were actually closer to a modern cozy.
The investigator has to be an amateur -- who is probably a big headache for the local law in that they keep meddling because they think the professional
investigators are ignoring critical clues and/or not competent.
There's often some semblance of a romance, but that's not to say that it IS a Romance
Investigators are almost always female, often single, and usually have a regular activity that means that it's not completely unbelievable that she keeps tripping over dead bodies.
I'm thinking a series when I say that -- think Jessica Fletcher of Murder She Wrote
who lives in the murder capital of Maine.
There are popular cozy series where the sleuth runs a bookshop, a bakery, an antique/used clothing shop, is a realtor, or delivery person. But there is also a series that features a chef as the amateur detective. He
works with a female professional detective. Which is a nice twist.
The amateur's specialized knowledge is often critical to the solution.
She (usually a she, as I said, so I'm sticking with that pronoun) may also have a sidekick. One or the other one is often single and looking . . . which is where the hint of romance often comes in. She may have a close friend or relative who is a more professional sort of investigator -- who spends most of the book telling her to stay out of it.
It's usually set in a small town, or in a very specific neighborhood of a larger city. Everyone knows everyone. Always suspect the strangers, but sometimes the killer is someone they've known all their lives or closely related.
The body doesn't have to show up RIGHT away, but there ought to be something weird that happens in the first chapter . . . maybe a mysterious something going missing or a break in or something like that.
Red Herrings are perfectly appropriate, but the reader must be able to figure it out based on clues provided.
The denouement is usually triggered by the main sleuth getting herself into trouble/putting herself in danger either on purpose or accidentally. But please, PLEASE, PLEASE
don't make her too stupid to live!