The writers of grammar books were preoccupied with certain contested constructions, such as the split infinitive, multiple negatives, the use of who/whom, etc. In some cases their judgments were based on a direct appeal to the equivalent usages in Latin, but in others they seemed to copy one another. The links below take you to digitized copies of the grammars identified, where you can read what they say about the distribution of "will" and "shall" among the first person, second person, and third person forms. No one seems to know where John Wallis derived the rule, but it does not seem to come from the usage of his contemporaries in the seventeenth century.
John Wallis, Grammatica Linguae Anglicanae , 1652
Even if you can't read Latin, you can make out the distribution from his examples at the bottom of p. 94 and top of p. 95.
Lowth, Robert. A short introduction to English grammar. Dublin, 1763. Search for what he says about shall and will.
Even Joseph Priestley, who in other matters heeded current usage, follows suit.
Joseph Priestley. The Rudiments of English Grammar adapted to the use of schools . London 1789.