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I think that two different considerations are typically conflated in this notion of "implicit" Baptism of Desire.

There's the idea of implicit desire for Baptism proper and then idea of implicit faith.

So, for instance, I am converted to the Church and want to become a Catholic, but I do not form the explicit intention "I desire to be Baptized."  One can see the DESIRE here to be implicit in the desire to become a Catholic.

Then there's the notion of implicit faith, which many have promoted.  "I am a well-meaning pagan who follow my lights regarding the natural law."

So this discussion gets confused the the degrees of "implicit"-ness, i.e. the degrees of separation from the explicit.

It's absolutely indisputed that supernatural faith is required for salvation.  Lots of modern BoDers focus on the "desire" (an act of the will) but ignore the intellectual requirements for salvation, as if one can will to have supernatural faith without believing anything.  What's at issue is what are the requirements to have supernatural faith.  Can faith be implicit in my desire to know God?  All theologians agree that SOME things must be explicitly believed, with the vast majority (and absolute unanimity before the year 1600) holding that explicit belief in the Holy Trinity and Incarnation were necessary for salvation.  In other words, no Jew, Muslim, or any kind of infidel can possibly be saved.

This was believed by all Catholics everywhere for the first 1600 years of Church history, meeting the criteria for infallible dogma based on the OUM.  Yet some Jesuits felt they were permitted to theorize that these were not necessary and that it was sufficient for supernatural faith just to believe in a God who rewards the good and punishes the wicked.  This was motivated by the desire to extend the possibility of salvation to infidels.

Of course, recent Novus Ordo developments hold that atheists can be saved without ANY explicit belief whatsoever.

I hold that Rewarder God theory is objectively heretical based on the teachings of the Ordinary Universal Magisterium.  Those who lived before Vatican II might be excused of formal heresy because the OUM had not clearly been defined, but this notion must now be rejected as absolutely heretical.

Lad, refresh my memory. What is the docuмent from Benedict XIV (?) in 1703 that ruled against the God that rewards principle the Jesuits were pushing?