That's about as good as my old Galen book, actually...
2182351 10-1/2" clutch A-833 1962-1964 B-body 361 383 413
The A-833 didn't exist until 1964. The 413 was not offered with a 4-speed in '62 or '63. It's quoted directly out of a newer Govier white book, with newer information. The only pre-'64 4-speed 413s were the two--that's right, two--1960 300F "letter cars" built with the Pont-a-Mousson four-gear manual. But yes, that bell would fit and function on a 413, 440, 400 or any other B/RB engine with the right associated parts... however, there's a completely different number for '64 4-speed cars, meaning Galen contradicts himself here. It's possible that some early '64 4-speed cars were built with the T-10 (availability problems with the new Chrysler trans?), but that transmission won't bolt to an A-833 bellhousing and vice versa.
Who knows? Likely, no one.
Here's one for you: when I destroyed the original Super T-10 in my '78 Trans Am, the replacement I found had a Chrysler input shaft. Now, the Super T-10 input shafts supposedly don't interchange with the old T-10s, yet I had a GM Super T-10 with a 1-inch, 23-spline input. GM used 10- or 26-spline input shafts. I had to piece the entire clutch assembly together from parts. I used a Pontiac pressure plate, Mopar disc, and Z/28 throwout bearing (if I recall, it was a collar-height issue) to make everything work. No one has ever been able to explain that trans to me, be it restoration expert or former racer.