Whether a particular sedevacantist sect has apostolic succession is entirely dependent upon the validity of the ordination of its priests and consecrations of its bishops however illicit. For example, each and every SSPX bishop has been excommunicated but they were each VALIDLY consecrated. Thus, regrettably, they have stolen the legitimate goods of apostolic succession. Each of the excommunicated bishops so created has the power go consecrate bishops and to ordain priests. For this crime of grand theft ecclesiastical, those bishops were excommunicated. They were illegally or illicitly consecrated but the consecrations were valid nonetheless.
Finally, the endless arguments by analogy to St. Catherine of Siena or to St. Athanasius or to the Eastern Orthodox are not apt and are simply puffery by SSPX. The validity of the SSPX Mass and sacraments were NEVER at issue but not by analogy to anything. Their bishops (not their priests) have genuine apostolic succession, however purloined, and that is the only issue as to validity. No one has claimed they lacked that succession. In fact the illicit possession of that succession is precisely the point of their perfidy.
BTW, I am aware of no mere priest who has been excommunicated formally for being of the SSPX although each may have excommunicated himself by adherence to the schism and each lay person adhering to the schism may have excommunicated himself or herself as well. Remember that is "adhered to the schism" not merely attended SSPX Masses.
The Jesuits were not excommunicated but suppressed in the 18th century or thereabouts for about 75 years. They apparently deserved to be suppressed. Some took refuge under the Russian Tsar Peter the Great. The trained me in the Faith way back when they were still Catholic. Nonetheless, they ought to be suppressed again since they have again become a collective viper in the bosom of the Church. Prudential errors are prudential errors not doctrinal ones.
Your proof of Mr. Gibson's ongoing involvement with SSPX or any sedevacantist schism or heresy or that he believes this pope wrong, please. For example: Who said the Masses on the set of the Passion? Is his daughter preparing for admission to some SSPX order of nuns or a Catholic order? Is his Los Angeles area chapel an SSPX chapel? How do you know this other than speculation?