Is seeking a sign a Buddhist divination?

No. But Buddhism has divination. For example, Dizang Cham Tea Classic. Although the prayer is not Buddhist, the bodhisattva can tell you the future through it in front of the bodhisattva. Manjusri Bodhisattva recorded it in the sutra of Hutuluo and others, but I forgot which one it was. Make it up later! Manjusri Bodhisattva didn't want to preach. Later, avalokitesvara advised her to tell her brother not to be greedy for fortune telling.