A couple of thoughts that crossed my mind when reading Sherlock Holmes: (I've read about 20 stories.)
My opinion (it's a pretty strong opinion) is ISTJ.
All this SP/Se talk is nonsense. I also agree with the introvert notion. He may be energized by 'being out,' but so many introverts are; it is not a good indicator of extroversion. He goes out, but not to be with people. Not EVER to be with people. He goes out because he must, to confirm or disconfirm his present theories.
The T couldn't be more obvious. Enough said, there.
The J is tricky. He does look a lot like a P, hangin' out until someone comes in with a problem. My main reason, stronger than any other by far, is a holistic one. I am convinced of the I and T, and the S almost as much, and he behaves a hell of a lot more like an ISTJ than an ISTP, in my opinion. Furthermore, as I've said, the Se idea makes little sense to me, whereas the Si makes a lot of sense. Think of how marvelous he is at connecting information back to similar circumstances. All of this has come from his fixation on physical detail - and his fine categorizations of those details. Even S's connect information together to form speculations, but the information they connect is or was physical, and that sure sounds like Holmes to me, and is decent justification alone for my 'S' opinion.
Good day, my dear bloggers.