Pope St Siricius' (died 399) understanding of the necessity of water baptism, and the rejection of BOD, is consistent with 99% of the Church Fathers. The main exception being St Augustine, who went back and forth on the topic, but in the end, rejected BOD. The entire "BOD question" originated with those who read St Augustine's pro-BOD position and theorized (but did not teach) that it might be possible.
From St Thomas, to St Bellarmine, to St Alphonsus --- all cite St Augustine. But St Augustine isn't enough for something to be "of Tradition". For something to be a doctrine, it must be traced back to Apostolic teachings, or Scripture. There's nothing in Scripture to support BOD and most of the Church Fathers rejected it (i.e. Apostolic teaching is against it).
Neither did Trent define it as a doctrine. Neither did Trent make the case that it is Traditional, or Scriptural, or Apostolic. In fact, Trent's quote of Scripture (where the Holy Ghost and water are necessary) condemns the whole idea. Trent's example of the 2 requirements for Baptism (i.e. Holy Ghost and water) correspond to the "desire" and the "sacrament" both being necessary. Not one or the other.
Absolutely. We had about 5-6 Fathers explicitly reject Baptism of Desire. St. Augustine very tentatively floated the idea as a youthful speculation but then forcefully retracted it in his post-Pelagian period and made some of the strongest anti-BoD statements in existence. St. Ambrose' oration was the other place that's cited in favor of BoD, but his meaning is far from clear. He stated elsewhere that not even the devout Catechumen can be saved unless he were regenerated in the Sacrament. I find the key in that he said of Valentinian that just as not even the martyrs are crowned, even if they are washed, hopefully Valentinian's piety / desire could have the same effect. But the key there is the "washed but not crowned", where crowning refers to entering the KINGDOM of Heaven.
St. Augustine's disciple St. Fulgentius also rejected BoD, and then you don't hear another word about BoD until it is revived by the pre-scholastics in the 1100s.
So the BoDers misrepresent the Patristic record here, with a couple anti-Feeneyite books making the absurd and mendacious claim that there was unanimous consensus of the Church Fathers in favor of BoD. BoB is a separate matter, where you had some Fathers claim that martyrdom was the only exception to the normal administration of the Sacrament, so an implicit rejection of BoD. But we needn't dwell on BoB here.
There's no evidence whatsoever that BoD was revealed.
So in the 1100s Hugh of St. Victor (pro BoD) was battling with Abelard (anti-BoD). Peter Lombard then asked St. Bernard for his opinion. He tentatively answered that he'd rather be wrong with St. Augustine than right on his own, simply relying on the "authority" of St. Augustine, who admittedly did not teach this with any authority, and evidently unaware that St. Augustine had retracted the opinion. Peter Lombard went pro-BoD, and his
Sentences then was a major influence on the scholastics, including St. Thomas Aquinas.
Pope Innocent II again deferred to the "authority of Augustine and Ambrose". As we have seen, neither of these authoritatively taught anything of the sort, with Augustine retracting and Ambrose's meaning entirely unclear, and IMO not teaching BoD at all, and he was certainly not teaching anything but merely expressing a hope in the possibility.
But when St. Thomas went pro BoD, that largely opened the floodgates.
So, the only way we can know something has been revealed (if not explicitly stated in Sacred Scripture) is ...
1) dogmatic / unanimous consensus of the Church Fathers
2) a doctrine derives necessarily (if not implicitly) from other revealed doctrine
We see clearly that #1 is not the case. If anything, there's near unanimous Patristic consensus against BoD, thought the Fathers didn't condemn it as heretical per se.
As for #2, I've never seen a doctrinal demonstration of it. We had arguments from "the Good Thief", which are faulty, since the Good Thief died before Baptism was made obligatory. St. Thomas explains that the Sacraments have both a visible and an invisible aspect, but doesn't demonstrate that they can be separated with regard to the effects of the Sacrament. Same thing applies to Confirmation, Holy Orders, Last Rites, that they have visible and invisible aspects, but it doesn't mean you can have Holy Orders of Desire.