When thinking about this question one must keep in mind the role of supplied jurisdiction in cases of common error. Even many sedevacantists have failed to do so and thus ended up with a slightly skewed view of things ...
Be that as it may, it seems to me that an episcopal appointment made by, say, Paul VI, would be valid if the appointee was capable of receiving it.
In this matter, it appears that the usually meticulously careful John Lane does not cite a source in support of what he says, either in the above excerpt or otherwise. Anyone who thinks otherwise is free to correct me here. For, appointment to an episcopal office is not a sacramental action that requires jurisdiction for its completion. How, then, can supplied jurisdiction be said to apply to this case? It appears those other sedevacantists, who maintain in my opinion, more correctly, that only those Bishops consecrated under Pope Pius XII would qualify as still possesing ordinary jurisdiction. There are several other reasons that can be cited in support of the same conclusion.
Of course that raises practical difficulties for those who espouse such a view, for it is known that only a handful of such Bishops, about 15 or so of them, still exist in the world.
John, I think I have answered one or more of your questions, but if you think otherwise, I will copy and paste the relevant portions of my replies immediately following your seven questions later on.
Malleus : Several Theories abound For example :
" What exactly is the Conciliar church? In order to answer that, let's ask ourselves, when was it founded, when did it appear in public, when did it achieve what many or most sedes assert - control of every see, every building, every "office" of the Church in all of their material elements?
I'd like Gabriele to tell us which Church the members of the hierarchy belonged to in, say, 1962, 1966, 1971, and 1980. Was every see possessed materially or de facto by an official of "the Conciliar church" in 1962? Any of the other dates? If so, on what basis is this assertion made?
The "default" attitude of trads, and especially of sedes, is to regard the entire official structure of the Church as Modernist, and then (perhaps) make exceptions. Even Archbishop Lefebvre adopted that view at least late in his life. And it's a legitimate and useful shorthand for the situation in which we have to live. But the theological, canonical, and properly ecclesiological approach must necessarily be the opposite. We start by adhering to the Catholic Church as it certainly was in 1955, just to pick an arbitrary date, and then we recognise that see after see was occupied by open Modernists as the revolution progressed. But many weren't occupied by open Modernists. Many were retained by what appear to have remained clearly Catholic men, such as Cardinal Siri in Genoa.
I certainly understand that for somebody who believes that Vatican II was manifestly heretical, all who accepted its docuмents as Catholic thereby left the Church, so that apart from Bishop de Castro Mayer perhaps, all sees fell vacant de jure at least in circa 1966. But that's not my view, and I doubt too many others really adopt it either. In any case it means that the hierarchy was extinguished at the latest in 1991 when de Castro Mayer passed away. Such a conclusion is heretical.
What seems to have happened is much more diffcult to explain, much more obscure. It seems apparent that it was possible to accept Vatican II, with reservations (as many bishops did), and even the chief reforms that followed in its wake (e.g. the new liturgy) without thereby leaving the Church. This seems to have been the case with Siri, Pintonello, Graber, and several others at least. Perhaps it was the case with hundreds of bishops. If so, where was "the Conciliar church"?
That's harder to answer, in such a scenario. I have an answer, and I have expressed it many times, over many years, and most recently in my article "Archbishop Lefebvre and the Conciliar Church", but I recognise that it isn't a simple answer. That is, I see that for people who are not familiar with ecclesiology, and with proper distinctions in general, it may not be convincing. "
Again my thanks to John Lane