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From the moment Sherlock rushed into someone's house without taking off her shoes, Wato knows that how Sherlock understands social etiquette is different from how most people do.
Her hypothesis is confirmed the other morning when Sherlock refuses the breakfast she made as the friendly gesture without thinking, and without a second thought after Wato explains it to her.
It makes Wato doubt their future as roommates because how can she live with someone whose behaviors are so unpredictable by common social standards? It's not that Wato has opinions about how people should or should not do, of course not. It's more like how one dances with another person; there's some rule to follow, and how can they manage it without making a disaster when they listen to different musical tones?
Besides, Sherlock seems all about logical thinking and reasonable deductions, but shouldn't be how socially people behave a part of her knowledge, too? Wato wonders while she exterminates the two portions of breakfast.
She can probably skip the lunch, at then she thinks.
At then she also thinks the unshakable feeling comes from her worry about herself in this new life. It takes her a while to realize that the one she worries about is, in fact, Sherlock, which might also be the reason why she keeps joining the investigation after the case of her beloved teacher.
Unknowingly, Wato makes it her self-assigned mission to be the interface between Sherlock and other people. Sherlock might not consider what she brings into the partnership as something important, but it never hurts to have someone to take care of it for her.
As they spend more time together, Wato realizes that Sherlock does know those things. She just doesn't put them into her consideration often, not letting them get in the way of her judgment. That's what Sherlock depends on to solve cases without being led to dead ends because of emotional or social biases. This discovery makes Wato more determined to stay by Sherlock's side because now she's more sure about her contribution in their relationship.
She is happy to be helpful.
Wato loves to think that by moving into this apartment, she's becoming a member of a group where they all have something to give to help Sherlock solving crimes, and her role is the translator. Although she always shoots back at Sherlock's childishness (well, sometimes she starts it, Wato admits, and she'll never pretend not to enjoy it,) Wato loves to see Sherlock in her full deduction mode as they approach the truth.
Also, as childish as Sherlock is, Wato finds out that she actually has her way to care about people.
One day Wato comes back to the apartment wondering whether Sherlock finishes her experiment yet. She doesn't want to be 'a distraction,' but at the same time, she's eager to know what Sherlock finds.
Wato sticks her head into the door cautiously and finds Sherlock still fully immersed in her work. Better to come back later, Wato thinks, but just when she decides to close the door, Sherlock says, "There are traces of poison" without turning her head.
"Poison?" Wato walks near the desk, curious.
It's after the case closed that it occurs to her Sherlock had already known the experiment outcome and was probably doing some further tests before she came in. So, Sherlock explained it to her for... updates? Or what? Wato isn't sure.
Another day Wato comes back late in the night. She is tired and feels a bit down. She enters the apartment and sees Sherlock standing by the door thinking out loud.
"Why was Natsuo Koda at the wedding?" Sherlock asks as if it's the most important thing at the moment, lifting a leg to block the way like a mischievous kid.
How long has she been standing there? Wato wonders.
When the epiphany finally sinks in Wato is embarrassed. How can she claim to understand how people behave socially better than Sherlock does, and more importantly, to understand Sherlock better than most people do when it takes her so long to get to the truth?
Given Wato's understanding of Sherlock, she isn't the kind of person who feels it's necessary (or comfortable for her, maybe) to say those greeting phrases, no matter how often they're used between close friends and families.
'I'm back,' to which Sherlock might say she already knows that 30 minutes ago because of some clues only she can pick up.
'Welcome back,' to which Sherlock might give her a look that means she's amused and bored at the same time.
But Sherlock does care about her presence in this apartment they share. Wato smiles at the realization.
Sherlock was waiting for her to come home. Because she'd found something and wanted to share just as how Wato wanted to know. Because it was late and she worried.
Those words are the closest thing to social etiquette and the most comfortable way for Sherlock to say it.
'Welcome home.'
She just solved a case on her own. Wato lets a big, proud smile bloom on her face before she opens the door.
"I'm home!"