Actually, the top trope I see everywhere is the classic "Stoic Detective Softens for You." It’s the bedrock of the ship. Writers love taking that iconic, detached intellect and building a scenario where the reader character—through sheer persistence, a shared case, or some mundane but endearing habit—becomes his one exception. He might start by deducing your entire life story from a scuff on your shoe, but then he'll keep your tea exactly how you like it without ever admitting he noticed.
A close second is the 'Forced Proximity' scenario. You get assigned as his new flatmate at 221B, or you're both trapped somewhere during a case. The tension comes from him having to navigate shared space, your belongings 'cluttering his mind palace,' and the inevitable late-night conversations by the fire. It’s a reliable engine for moving from professional annoyance to reluctant fondness.
I also see a lot of 'Injured/Comfort' fics. He’s the one who gets hurt, and the reader has to patch him up, leading to uncharacteristic vulnerability. Or, inversely, the reader is in danger, and his usually controlled panic reveals depths he’d never voice. The appeal is in that crack in the armor, the moment his hands aren't quite steady while applying antiseptic.
There’s a niche but persistent trend for 'Baker Street Ghost' or 'Soulmate AU' fics too, where the reader is the ghost of a past client or a modern person who wakes up in Victorian London. It lets writers play with the canon setting while inserting a reader with modern sensibilities that constantly baffle and intrigue him.