The second person of will and shall are wilt and shalt in the archaic form. The third person singular suffix is -eth, so we get willeth but what about shall?
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Willeth is used as a transitive verb ("La Reine le veult," "The Queen wills it", as Parliament has the Royal Assent).
We don't get willeth for will as a modal auxiliary indicating future action. These verbs don't change; similarly shall and must don't change either.