Interesting usage by Unamuno here during his barracking by the Falangists. He seems to be drawing the same contrast between ‘to persuade’ and ‘to convince’ that I intuitively discerned as allogenic and autogenic.
Millán-Astray responded: "¡Muera la inteligencia! ¡Viva la Muerte!" ("Death to intelligence! Long live death!"), provoking applause from the Falangists. Pemán, in an effort to calm the crowd, exclaimed"¡No! ¡Viva la inteligencia! ¡Mueran los malos intelectuales!" ("No! Long live intelligence! Death to the bad intellectuals!")(from Wikipedia Unamuno)
Unamuno continued: "This is the temple of intelligence, and I am its high priest. You are profaning its sacred domain. You will win [venceréis], because you have enough brute force. But you will not convince [pero no convenceréis]. In order to convince it is necessary to persuade, and to persuade you will need something that you lack: reason and right in the struggle. I see it is useless to ask you to think of Spain. I have spoken." Millán-Astray, controlling himself, shouted "Take the lady's arm!" Unamuno took Carmen Polo by the arm and left in her protection.
Yes of course it’s Spanish but being a Romance language it stays even closer to Latin roots. Reason and right have to find a resonance in the person whom you are trying to persuade. This arising from within produces conviction.