Pertinacity deals more with PERSISTENCE than with sincerity. We can't judge the internal forum, only the external ... which is why the theologians discussing the possibility of a Pope vacating the See due to heresy speak of "MANIFEST" heresy.
That's fine but who has judged the conciliar popes persistence in manifest heresy?
Also, at what precise moment did John XXIII become a formal heretic and lose his office? Who determines that?
Paul VI?
John Paul II?
Benedict XVI?
Francis?
It seems arbitrary.