"TO A T - a possible origin suggests that the T stands for "Title", a minute and precisely positioned pen stroke or printer's mark. A tiny brushstroke was all that distinguished the Hebrew letter "dalet" from "resh". "Title" was the word chosen by Wycliffe to translate references to this tiny difference in his version of the New Testament. Thus the mark was perfectly suited to its task."
"PAT -- From "The Dictionary of Etymology: The Origins of American English Words" by Robert K. Barnhart (HarperCollins, 1995): "pat2 adv., suitably. 1578, perhaps a special use of pat1 (a light tap), in the sense of hitting the mark; and thus 'opportunely,' ready for any occasion."