So I'm pretty sure that Holmes wasn't ever in the middle of indexing his records, heard a jaunty tune start up, and leap to his feet to start dancing.
But "Red-Headed League" definitely tells us something about Mr. Sherlock Holmes:
"All afternoon he sat in the stalls wrapped in the most perfect happiness, gently waving his long, thin fingers in time to the music, while his gently smiling face and his languid, dreamy eyes were as unlike those of Holmes the sleuth-hound, Holmes the relentless, keen-witted, ready-handed criminal agent, as it was possible to conceive."
That finger waving tells us something. That's a man who wants to move his body.
You've been there, I hope. That place where the music takes you, but the situation won't allow full-out dancing. (Whoever invented the stand-up desk did not accounted for what happens when said worker at said desk starts getting into the music coming into their ear-buds.) But Sherlock Holmes was probably not the kind of guy who went to a dance hall, formal dance, or one of the other places Victorian London encouraged dancing to happen. So where was all that pent-up energy to be released?
I think John Watson pretty much told us in that same story, just before we get to the finger-waving.
"My friend was an enthusiastic musician, being himself not only a very capable performer but a composer of no ordinary merit."
An enthusiastic musician.
The very first thing that Sherlock Holmes brings up when discussing becoming room-mates with Watson isn't his very strange occupation, criminals, etc. No, the first thing Sherlock checks out with John is whether or not his violin playing is okay. He loves his violin.
And why does he love his violin? Because Sherlock Holmes plainly loves music.
And what does the violin offer that some instruments don't? A whole lot of physical movement while playing. It doesn't take much time on YouTube to see how many young violinists get into rocking out while playing their fiddle. Given the energy with which he through himself into every other aspect of his life, you know Sherlock Holmes threw himself into playing that violin.
Even though Watson never specifically writes it out, you have to know Sherlock Holmes was a dancer. Art in the blood may take the strangest forms, but music in the blood tends to take at least one specific, fluid form. It only makes sense that as he has expanded into the many lives he's leading in fic that Sherlock Holmes has been cast as a professional dancer more than once. The man had it in him.
Those dancing gray eyes of mirrored a dancing soul, even in a time when you had to make your own music just to cut loose.