One of the great misunderstanding concerning how the term "rule of faith" works before the early modern period is the idea that it refers to the question of ruling or governing authorities or sources. The rule of faith debate in the early modern period normally oscillates between tradition or Scripture, debating which gets to govern or norm the faith.
But if you see how the term "rule of faith" is used before that, you'll note that that's a category confusion. The "rule of faith" does not refer to authority of sources but rather the logic or structure of the subject matter/contents of the faith. They are more akin to logic rules or differentiation rules in mathematics, or Kirchhoff's Rules in physics for calculating currents and potential difference in a circuit, rather than rules of an external governing authority. Differentiation rules describes the logic of differentiation and prescribes mathematical procedures for differentiating a function, it is not a rule which is valid by virtue of the authority of your teacher or Newton or Leibniz.
To appreciate this point we need only turn to Tertullian who uses the term "rule of faith" more than most other Fathers. He says:
Now, with regard to this rule of faith— that we may from this point acknowledge what it is which we defend — it is, you must know, that which prescribes the belief that there is one only God, and that He is none other than the Creator of the world, who produced all things out of nothing through His own Word, first of all sent forth; that this Word is called His Son, and, under the name of God, was seen in diverse manners by the patriarchs, heard at all times in the prophets, at last brought down by the Spirit and Power of the Father into the Virgin Mary, was made flesh in her womb, and, being born of her, went forth as Jesus Christ; thenceforth He preached the new law and the new promise of the kingdom of heaven, worked miracles; having been crucified, He rose again the third day; (then) having ascended into the heavens, He sat at the right hand of the Father; sent instead of Himself the Power of the Holy Ghost to lead such as believe; will come with glory to take the saints to the enjoyment of everlasting life and of the heavenly promises, and to condemn the wicked to everlasting fire, after the resurrection of both these classes shall have happened, together with the restoration of their flesh. This rule, as it will be proved, was taught by Christ, and raises among ourselves no other questions than those which heresies introduce, and which make men heretics.
- The Prescription against Heretics
What is the "rule of faith" here? It isn't "Scripture" or "Tradition", the rule of faith here refers directly to the subject matter of the faith itself, e.g. monotheism, the incarnation, the events of Christ's life, etc, etc. It is these propositional content which "rules" how are to reason about the faith and make our inferences. We can see this again in Augustine:
Receive, my children, the Rule of Faith, which is called the Symbol (or Creed ). And when you have received it, write it in your heart, and be daily saying it to yourselves; before ye sleep, before ye go forth, arm you with your Creed... These words which you have heard are in the Divine Scriptures scattered up and down: but thence gathered and reduced into one, that the memory of slow persons might not be distressed; that every person may be able to say, able to hold, what he believes.
- A Sermon to Catechumens on the Creed
The rule of faith here again is simply the creed which summarises the events and propositions gathered from Scripture. Finally in Athansius we see:
For there are things called eternal of which He is Framer; for in the twenty-third Psalm it is written, 'Lift up your gates, O you rulers, and be lifted up, you everlasting gates ;' and it is plain that through Him these things were made; but if even of things everlasting He is the Framer, who of us shall be able henceforth to dispute that He is anterior to those things eternal, and in consequence is proved to be Lord not so much from His eternity, as in that He is God's Son; for being the Son, He is inseparable from the Father, and never was there when He was not, but He was always; and being the Father's Image and Radiance, He has the Father's eternity. Now what has been briefly said above may suffice to show their misunderstanding of the passages they then alleged; and that of what they now allege from the Gospels they certainly give an unsound interpretation , we may easily see, if we now consider the scope of that faith which we Christians hold, and using it as a rule, apply ourselves, as the Apostle teaches, to the reading of inspired Scripture.
- Discourse 3 Against Arians
Using what as a rule? Using tradition or even Scripture as a rule? No, it is using the actual subject matter and propositional content, e.g. the eternality of the Son, as a rule to read the Scriptures. It is these specific propositional claims which are the "rule of faith", not an external formal authority or source regardless of its contents.
This point can be hammered in when we look at how Aquinas uses the term "rule".
Now the formal object of faith is the First Truth, as manifested in Holy Writ and the teaching of the Church, which proceeds from the First Truth. Consequently whoever does not adhere, as to an infallible and Divine rule, to the teaching of the Church, which proceeds from the First Truth manifested in Holy Writ, has not the habit of faith, but holds that which is of faith otherwise than by faith.
– S.T. 2.2.5.3
While we might be tempted to think that “adhere, as to an infallible and Divine rule, to the teaching of the Church” refers to the infallibility of the Magisterium of the Church, however we should already be wary of such an inference given how "rule" operates. Remember, he's speaking here of the teaching of the Church, not the teachers of the Church, it is the propositional content, the teaching itself, which is the rule, not the teachers. This becomes very obvious when we note what he says elsewhere concerning the same subject:
We cannot know anything about the truth except on the basis of the first principles and in the light of the intellect, which cannot manifest the truth except inasmuch as they are a likeness to the first truth, since from it they have a certain immutability and infallibility. All truths are not seen in this life in the first truth according to essence, given that neither is the first truth seen by us in this life in its essence. However, every truth is known in it on account of its image, that is, on account of the truth copied from it.
- Quodlibet X. q4. a. I
This is a remarkable passage because it shows the metaphysical and realist background Aquinas is operating on which determines the “infallibility” of first principles. It is “infallible” not because it has been promulgated by the authority of the Magisterium of the Church or the promise of Christ to the successors of Peter; its infallibility is derivative of its ontological and metaphysical resemblance to God, the First Truth. By “resembling” the First Truth, first principles acquire bits of its immutability and infallibility. As such, infallibility is a relationship which obtains between the different realities which logically, or more accurately, ontologically flows from the First Truth, that is to say, it is a relationship which obtains between the propositional content of the “teachings of the Church”. It has nothing to do with the Magisterium being able to provide infallible epistemic certainty. This is how the teachings of the Church can acquire its infallibility and is an "infallible rule", because it is derivative of the First Truth, i.e. God himself.
As such, the whole debate about whether the rule of faith refers to the tradition or Scriptures is basically a historical confusion and misstep, conflating early modern concerns about epistemology with pre-modern concerns about the logic and structure of the subject matter of the faith. But once we review the actual primary sources, the logic becomes a lot clearer.