Honestly, a lot of writers think adding a Cheshire Cat-inspired OC is just about them having a creepy grin and making cryptic comments, but that ends up feeling like a shallow imitation if you're not careful. The whimsy doesn't come from the cat itself, but from how it warps the logic of your story's world. If your plot is a straight line from A to B, this character should be the one casually suggesting there's a C, an F, and a sideways Z that nobody considered.
I tried writing one for a fantasy mystery, and the real challenge was letting the cat be genuinely disruptive, not just a quirky sidekick. It would give the hero advice that seemed nonsensical but, three chapters later, would turn out to be the key—not because the cat knew the future, but because it operated on a completely different set of cause and effect. The plot had to become more fluid, with solutions appearing from bizarre angles. That's the whimsical engine: it forces your plot structure to become less rigid.
On a more practical level, its appearances and disappearances can be great for pacing. Need to drop a major clue without it feeling forced? The cat can fade in, drop a riddle, and vanish, leaving the characters (and readers) to piece it together. It turns exposition into a puzzle, which is way more fun than having a standard wise old mentor explain everything.