Conciliar infallibility has been understood in the Church since its beginning, and Vatican II did not invent this doctrine; it merely put it into writing in a General Council. If General Councils were not infallible, then how would you know that Papal Infallibility is an infallible truth? That the Church when gathered together in a General Council in union with the pope is infallible is rooted itself in Scripture, as in the first Church Council at Jerusalem the inspired author of Scripture reports the apostles saying, “It has seemed good to the Holy Spirit and to us.”
The citation from the Catholic Encyclopedia (CE) written before Vatican II clearly explains that General Councils are infallible, and Vatican II did not define any new teachings, as Paul VI repeatedly explained. I’m guessing you haven’t read the CE article yet. No General Council was needed to explain that General Councils are infallible, as the Church has always understood this fact. Here is the relevant section on Conciliar infallibility:
“That an ecumenical council which satisfies the conditions above stated is an organ of infallibility will not be denied by anyone who admits that the Church is endowed with infallible doctrinal authority. How, if not through such an organ, could infallible authority effectively express itself, unless indeed through the pope? If Christ promised to be present with even two or three of His disciples gathered together in His name (Matthew 18:20),
a fortiori He will be present efficaciously in a representative assembly of His authorized teachers; and the Paraclete whom He promised will be present, so that whatever the council defines may be prefaced with the Apostolic formula, “it has seemed good to the Holy Ghost and to us.” And this is the view which the councils held regarding their own authority and upon which the defender of orthodoxy insisted. The councils insisted on their definitions being accepted under pain of anathema, while St. Athanasius, for example, says that “the word of the Lord pronounced by the ecumenical synod of Nicaea stands for ever” (Ep. ad Afros, n. 2) and St. Leo the Great proves the unchangeable character of definitive conciliar teaching on the ground that God has irrevocably confirmed its truth “universae fraternitatis irretractabili firmavit assensu” (Ep. 120, 1).”
newadvent.org/cathen/07790a.htm#IIIA
The article goes on to explain that the Anglicans opposed the Church’s teaching on Conciliar infallibility through denying the teachings are correct until accepted by the people, so clearly the Church was teaching that General Councils are infallible long before Vatican II.
It does state which teachings fall under the category of infallibility though it did not list every one. First, if the Church defines a teaching under the pain of anathema, then clearly it is infallible. Hence, the doctrinal canons of General Councils are infallible. Second, in the content of the Council’s writings there can be some theological explanations as to why a particular teaching is true. I remember reading that these explanations are not safeguarded from error. However, the definitive teachings themselves most certainly are infallible.