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This is absolutely correct.  THIS is where private judgement has a legitimate role, in examining the motives of credibility.

“Private judgement” is necessary in all aspects of life and faith. In reality, hierarchical ecclesiastical authority is limited to determining what constitutes the articles of faith, what is opposed to the aforementioned, protecting the Church from pernicious matters opposed to the faith, and by creating temporal-spiritual disciplines to safeguard the Church and the faithful in all aspects of life as it relates to faith and morals.

Everything else is “private judgement.”

-Knowing that the Catholic Church is the one true Church.
-Knowing that the articles of faith have historic apostolic continuity.
-Knowing that a man at a given time is Pope.
-Knowing that the Pope really said X.
-Knowing how to understand and interpret a Papal or Church statement on any matter.

All of this requires the mind and these matters are only as certain as the mind of the person understanding them. There is an objective reality and it is only through intellect that we can know what it is and its certainty is dependent on the mind that reached it.

The indefectibility of the Church is related to the de fide credenda dogma of the perpetuity of Papal succession defined in the Dogmatic Constitution of the Church “Pastor aeternus.” The dogma of the indefectibility of the Church is moreover closely related to the doctrine of the permanence of the Church, and although it has not been proclaimed in an independent extraordinary decree of its own, it is considered a secondary object of the infallibility of this teaching, and as such, is a tenenda infallible teaching in its own right. The indefectibility of the Church is listed by Dr. Ludwig Ott as a sententia theologice certa (“theologically certain teaching” or Sent. certa.) dogma, meaning that it is a teaching that the Magisterium has definitively proposed. The dogma of the indefectibility of the Church has been summarized as follows: “The Church is indefectible, that is, she remains and will remain the Institution of Salvation, founded by Christ, until the end of the world” (XIV).

I'm not sure why you wrote this in reply to my earlier post, but there are a few minor errors in what you wrote that I will clear up.  First, permanence of the Church (which is an aspect of the Church's promise of indefectibility), is not a secondary object of infallibility. It is a primary object (a revealed truth - Mt 28:20)), and, even if it has not been solemnly defined by a single definitive act, it is certainly a truth that has been infallibly proposed by the force of the ordinary and universal magisterium.

A secondary object of infallibility is a truth that has not been revealed, but which is necessary to preserve the revealed deposit.  The assent "tendendas" (to be held) is owed to secondary objects that have been definitively proposed.  The assent owed to a primary object of infallibility that has been infallibly proposed by the ordinary and universal magisterium (such as the doctrine of the permanence of the Church) is that of divine and Catholic faith.

But since you agree that the perpetuity of papal succession is de fide, do you believe there as been perpetual successors of Peter up to the present day, or do you believe the last Pope died 65 years ago?

I'm not sure why you wrote this in reply to my earlier post, but there are a few minor errors in what you wrote that I will clear up.  First, permanence of the Church (which is an aspect of the Church's promise of indefectibility), is not a secondary object of infallibility. It is a primary object (a revealed truth - Mt 28:20)), and, even if it has not been solemnly defined by a single definitive act, it is certainly a truth that has been infallibly proposed by the force of the ordinary and universal magisterium.

A secondary object of infallibility is a truth that has not been revealed, but which is necessary to preserve the revealed deposit.  The assent "tendendas" (to be held) is owed to secondary objects that have been definitively proposed.  The assent owed to a primary object of infallibility that has been infallibly proposed by the ordinary and universal magisterium (such as the doctrine of the permanence of the Church) is that of divine and Catholic faith.

But since you agree that the perpetuity of papal succession is de fide, do you believe there as been perpetual successors of Peter up to the present day, or do you believe the last Pope died 65 years ago?

Yes, the permanence of the Church is a primary object of infallibility. I was referring to indefectibility as a secondary object of infallibility closely related and necessary for the dogma of permanence.

I believe there have been perpetual successors of Peter and there will continue to be such. The last Pope, Pius XII, passed away and there has been an interregnum of 65 years that will be resolved in due time. This is no different than the death of a Pope and the time it takes to elect another as has already been said about this ad nauseam.

I do not believe in Ecclesiavacantism.