Objection 1: Pope Pius XII lifted all ecclesiastical penalties during the conclave to elect the pope. So even if the Vatican 2 popes were heretics before their elections, they would still be validly elected.
Answer: Heretics and schismatics are barred by DIVINE LAW from the election to the Papal Office. Pope Pius XII lifted ecclesiastical penalties. He did not, would not, could not dispense from Divine Law. 
Proof:
A. Institutiones Iuris Canonici [1950]
B. Institutiones Iuris Canonici [1921]
C. cuм Ex Apostolatus Pope Paul IV
D. Institutiones Iuris Canonici [1921]

Objection 3: If all the Vatican 2 popes were invalid, then there would be no cardinals to elect a future pope. Thus the papacy would come to an end which is impossible. 
Answer: During the Western schism, three men claimed to be pope (the true pope in Rome, one in Avignon and one in Pisa). In order to heal the nearly forty-year schism, the Council of Constance determined that with all the cardinals, delegates from each country would participate in the papal election (Pope Martin V was elected). Theologians teach that in doubt of or absence of cardinals, THE CHURCH HAS THE RIGHT TO CHOOSE ITS HEAD.
Proof
A. De Potestate Ecclesiae
B. De Comparatione Auctoritatis Papae et Concilii
C. De Ecclesia Christi
D. The Church of the Incarnate Word

Great series of posts! 

Obviously, under “proofs”, I left out the citations, as that would have made these posts much lengthier and time consuming. In discussion, I could post any quotes necessary. 

The video conference from Bishop Pivarunas discussing this booklet is even better than the booklet itself. Here is that link to that video. 

https://youtu.be/vSkwPiqyv-k?si=nR34R9S0nIBvdV-L

Objection 1: Pope Pius XII lifted all ecclesiastical penalties during the conclave to elect the pope. So even if the Vatican 2 popes were heretics before their elections, they would still be validly elected.
Answer: Heretics and schismatics are barred by DIVINE LAW from the election to the Papal Office. Pope Pius XII lifted ecclesiastical penalties. He did not, would not, could not dispense from Divine Law.
Proof:
A. Institutiones Iuris Canonici [1950]
B. Institutiones Iuris Canonici [1921]
C. cuм Ex Apostolatus Pope Paul IV
D. Institutiones Iuris Canonici [1921]

I have always heard from totalist sedevacantists that divine law prevents a heretic from becoming Pope, but which divine law are they referring to?

I have always heard from totalist sedevacantists that divine law prevents a heretic from becoming Pope, but which divine law are they referring to?

This is part of the reason why the crisis is the greatest crisis the Church has ever seen. The root of the crisis has and will always be poor catechetics. Many do not even know what a Catholic is. What does it mean to be a Catholic. To be Catholic (apart from being baptized) means that you profess and believe all the Divine truths of the Catholic religion. It means that if one were to deny even one of those Divinely revealed truths, they would cease to be Catholic. And once one ceases to believe in the Catholic Faith (no longer being Catholic) one cannot be the spiritual leader and head of Catholics. DIVINE LAW. We are not talking about the decalogue here. We are talking about divinely revealed Truths. If one were to assert that a non-Catholic and non-member of the Catholic Church could be its spiritual leader and Vicar of Christ, the result would be madness. You would see the fruition of a masonic religion based on indifference and feel good policies. Essentially, you would have Francis. 

I have always heard from totalist sedevacantists that divine law prevents a heretic from becoming Pope, but which divine law are they referring to?

By divine law, they're referring to simple definitions and ontologies, i.e. someone who's not a member of a body cannot be its head.  St. Robert Bellarmine characterizes the fact that a manifest heretic cannot be pope as rooted in divine law.  You do realize, right?, that divine law doesn't mean that God descended from Heaven and issued some legislation, but that some principle derives from revelation, e.g., in this case, the very nature of the Church.

My response:

https://www.cathinfo.com/crisis-in-the-church/response-to-all-the-sede-threads/