Why don't we just use the unbiased photographs we have of him?
Why don't we just read the interviews people made with him?

But seriously, I reckon that music at the time was greatly influenced by the zeitgeist of the period, so to classify J. S. Bach as a certain type based on his music is to try to apply Socionics theory to categorise his music (not illegitimate, but you're not typing the person), which would be probably more useful for assigning a type to the style of music of the period.

I don't know why, but it seems that Baroque Music, Classical Music, Romantic, 20th, pretty much made up all of the music of their respective periods, whereas now people can write in any style and often vary, so how people write in the past is probably more indicative of the era rather than themselves.

Secondly, I know musicians who write different styles of music based off different eras - implicitly here I'm saying that I can't identify any Socionics IEs in their different positions - so I don't think what people write is necessarily related to how they are as a person.