The 'tittle' suggestion in the above link is almost certainly the right derivation, one meaning of ‘tittle' being the cross-mark on the letter 't' and other such small elements of writing such as dots. The Oxford English Dictionary rejects all of the other so-called possibilities as untenable.
When writing in a hurry, one often omits the cross-stroke of a 't' or the dot above a ‘j' or ‘i', so 'to a T' suggests something is exactly right.
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