Fr Wathen was very clear that he was against sedevacantism, 1) because none us has authority to decide, 2) it's a distraction from our daily duties to God.  I don't know if Fr was ever confronted with the term 'sedeprivationism'; I would think he would agree with it (as he obviously believed its details).  But he always seemed more concentrated on dealing with the Great Conspiracy, which affects ALL aspects of society (the Church, politics, society, the economy etc), much more than just the papal question.

1) No serious Catholic who holds the sedevacantist position, that I know of, ever claimed to have any authority to decide, with authority, the papal question. We merely are taking Catholic principles from the vast majority of authorities (popes, theologians, Doctors of the Church) and applying them to the crisis we find ourselves in today.

2) It is not a distraction since it is the absolute duty of every Catholic to submit ourselves and to be subject to the reigning pontiff.

Actually he had it backwards, the ”Conspiracy” pales in importance when comparing it to the crisis in the Church and also to the papal question. Thankfully, it was the ”Conspiracy” that God used, in part, to bring me to tradition. After that, I paid less attention to political affairs and much more to religious ones.

Just because Father Wathen was a good and honorable priest that didn’t go along with the changes in the Church, it doesn’t mean that he was an infallible guide and that his opinion was perfect.

Certainly not in the Conciliar Church, which clearly lacks the marks.

That's not an answer, but it's what I expected you to say.

To paraphrase +Tissier, the Catholic Church remains among those baptized Catholics who still profess the true faith.

Very bad/heretical answer.  The baptized who profess the faith are only the material cause.  The material cause is only one of the marks (catholicity).  

Due to the fact that it's temporarily headless, like in any sedevacante period, it remains in eclipse (as per Our Lady of La Salette).

It's not headless, and when it is (during an interregnum), the Church is not eclipsed.  It is still visible and it continues to possess the marks.

It's hidden behind this false Church that has emerged.  "The Church will be in eclipse.  Rome will lose the faith and become the seat of the Antichrist."

The Sun of the Church's brilliance is hidden behind the moon of corrupt men, who have temporarily blocked its light from shining.  During an eclipse the location of the Sun doesn't change.  It remains where it was before the light was blocked, and it gradually reappears in the same location as the obstacle is passes by.  So too, the Church remains where it was before the crisis broke out, and its light will again shine forth - and indeed is already beginning to shine forth, in spite of the last gasp and final efforts of its enemies.    

If there is one visible head and one hierarchy over two distinct Churches, and if both Churches have most of the same members, how can a Catholic separate from communion with the Conciliar Church without at the same time separating from communion with the Catholic Church?  

The answer is simple: because the True Church's doctrines, liturgy and traditions still exist, are still legal and there are bishops/priests to whom the faithful can go to follow them.  The Conciliar Church has setup a "parallel" system with "new understandings" of doctrine, with "new usages" of the liturgy and "updates for modern man" to Her traditions.  The True Faith is still obligatory, both morally and legally.  The conciliar system is not obligatory at all, neither morally nor legally.

Praeter If there is one visible head and one hierarchy over two distinct Churches, and if both Churches have most of the same members, how can a Catholic separate from communion with the Conciliar Church without at the same time separating from communion with the Catholic Church?  

Pax Vobis The answer is simple: because the True Church's doctrines, liturgy and traditions still exist, are still legal and there are bishops/priests to whom the faithful can go to follow them.  The Conciliar Church has setup a "parallel" system with "new understandings" of doctrine, with "new usages" of the liturgy and "updates for modern man" to Her traditions.  The True Faith is still obligatory, both morally and legally.  The conciliar system is not obligatory at all, neither morally nor legally.

But if the hierarchy and members of the two Church's are the same, a person cannot separate from the hierarchy and members of the Conciliar Church without separating from the hierarchy and members of the Catholic Church.  If the two are one, you cannot separate from one without separating from the other.

But let's apply what you wrote to the two Church theory to see how a partial separation could take place.

1) There is one pope and hierarchy over two Churches - the Catholic Church and the Conciliar Church.  Therefore, to remain a Catholic, it is necessary to remain in union with the Pope and hierarchy of the Catholic Church, even though the same men are also the Pope and hierarchy of the Conciliar Church.  If a Catholic separates from the Pope and hierarchy of the Conciliar Church (which is also the hierarchy of the Catholic Church), he is at least a schismatic (and probably also a heretic), and definitely cannot be saved ("submission to the Pope is necessary for salvation," etc.)

2) In order to remain faithful to the Catholic Church, one must retain the true doctrines, the traditional liturgy, and the traditions, all of which are still legal. To avoid the Conciliar Church, the Catholic must avoid any doctrinal errors and novelties contrary to tradition, none of which are obligatory or morally binding anyway.

3) Conclusion: To be a true Catholic and to save you soul, you must be in union with the Pope and your local Novus Ordo bishop, you must retain the true doctrine, traditions and liturgy, and you must avoid the errors and novelties.

Based on this exercise, who other than myself is a true Catholic?

1) There is one pope and hierarchy over two Churches - the Catholic Church and the Conciliar Church.  There
fore, to remain a Catholic, it is necessary to remain in union with the Pope and hierarchy of the Catholic Church, even though they same men are also the Pope and hierarchy of the Conciliar Church.  

Well, you'll have to define "being in union with".  I would define it as being in union with "Eternal Rome" first (i.e. true doctrine).  If the case arises where the pope/hierarchy are quasi-heretical, then 1) they are the ones not in union with Eternal Rome and unchanging, Divine Truth.  2) As Trads have always said, "You used to believe as we do.  We are the same; you are the ones that changed."  3) Faith is greater than obedience.  No man can make you sin, nor deny doctrine.  4) Truth is our Authority; the hierarchical authorities are not Truth.

If a Catholic separates from the Pope and hierarchy of the Conciliar Church (which is also the hierarchy of the Catholic Church), he is at least a schismatic (and probably also a heretic), and definitely cannot be saved ("submission to the Pope is necessary for salvation," etc.)

Traditionalists (of all kinds) have only separated themselves from the conciliar, parallel system.  This is not schismatic because 1) the conciliar, new-age "spiritualism" is not obligatory, and it's actually illegal and immoral (contrary to Quo Primum).  Since the V2 popes have NEVER commanded that ANY catholic attend the new mass, or accept V2 with any 'certainty of faith' so we are allowed, both morally and legally, to avoid these areas without schism.  Trads are under the law, even if new-rome acts like the law doesn't exist. 

2) In order to remain faithful to the Catholic Church, one must retain the true doctrines, the traditional liturgy, and the traditions, all of which are still legal. To avoid the Conciliar Church, the Catholic must avoid any doctrinal errors and novelties contrary to tradition, none of which are obligatory or morally binding anyway.

Agree.

3) To be a true Catholic and to save you soul, you must be in union with the Pope and your local Novus Ordo bishop, you must retain the true doctrine, traditions and liturgy, and you must avoid the errors and novelties.

You are in union with the pope and bishops by accepting the reality that they occupy the offices.  To denounce their heresies is not schism.  To avoid their scandals is not schism.  To attend private masses of real priests, who say the True Mass as legally allowed by Quo Primum is both morally and legally allowed and required.

Based on this exercise, who other than myself is a true Catholic?

The Truth is not based on numbers.  The "fewness of the saved" is both a reality and a sobering mystery.  Let's pray that we all persevere in the Truth we were mercifully given.

3) Conclusion: To be a true Catholic and to save you soul, you must be in union with the Pope and your local Novus Ordo bishop, you must retain the true doctrine, traditions and liturgy, and you must avoid the errors and novelties.

I’m curious, what kind of “union” are you inferring that we are to have with your putative pope and ”Novus Ordo” bishop? Why don’t we profess the same faith if we are members of the same church?

Then what Church possesses them?  The "NO Church" is the only candidate.  

It demonstrably does NOT possess the marks.  It has only material Apostolicity, but not formal Apostolicity (cf. the Catholic Encyclopedia article on Apostolicity).  It certainly lacks Holiness, as its central act of Public Worship is anything but holy, is displeasing to God, and harmful to faith.  It has geographic Catholicity but has ruptured in time with the past Traditional Church.  As for being one, 95% of the NO are cafeteria Catholics, and there's hardly anything that resembles unity of belief in the Church.