I'm coming closer to a technical refutation of sedevacantism.
Most people, in debating sedevacantists, do not take the claims of sedevacantists seriously, and end up saying something like, "that's crazy; that can't be true; God wouldn't let that happen." When the logic isn't directly refuted, sedevacantists take that for further proof of their own claims.
The key claim of sedevacantists is that of contradiction. Their method is deductive logic; their premises are external words; are definitions and concepts; are abstract; are not concrete things, but intelligible species; are not full realities.
But man first understands (grasps intelligibility) in images; phantasm. This is pre-conceptual; is intelligent, not logical. Man understands something of the form in the diagram of a circle before he defines. After this grasp proceeds the inner word that is the beginning of definition and judgement. Spoken words refer to inner words; written words are symbols for spoken words.
So, sedevacantists are intelligent, reasonable people making logical deductions from abstract definitions, which were themselves verbalizations proceeding from individual minds grasping intelligible forms in concrete, particular things and historical situations. Since sedevacantists do not account for all of concrete reality, they operate at the level of a critique. But Kant made valid critiques; Hegel, Nietzsche, Marx, et al, made certain valid critiques, as they also used their faculty of reason and did not speak only nonsense.
Sedevacantists understand something of the evil in the human elements of the Church, but we need not accept this as a demonstration that the Church, headed by Francis, is not, ontologically, the Roman Catholic Church.
I will continue to develop this, but I see now a technical explanation of my first notion, months ago, that sedevacantists cannot be refuted on the terms they set up. More than the level of logic is involved in theology, and to say that is not to prescind at all from an intelligent refutation.
Conceptualism is a myth, and can be shown to be so. One sees this water, then that water, and so decides that there must be an ideal water in a noetic heaven that this or that water is imperfectly imitating. Somewhere there's an Idea of true water; personify the Idea and call him Neptune.
But the Aristotelian-Thomist account shows that while there is common matter (intelligible species), abstracted from particular things, from which we grasp forms, these are merely parts of the real; parts abstracted from space and time, understood and communicated apart from space and time.
The teachings of the Church are not subsistent Ideas against which real men and societies must be compared. The teachings are external words, abstracted and defined from concrete situations, to facilitate understanding any present or future concrete situation. Grasping a particular good of order in the Roman Empire results in the abstract definition known as civilization. Civilization as divine Idea leads to declaration that all others are barbarous abominations. Using the concept 'civilization' to pick out the particular good of order in this or that particular society, present or future, allows for discovery and encouragement of further good in potency that may be actualized.
Insofar as a sedevacantist is a conceptualist, he remains in his holding pattern; caught in myth; unable to see that this Church is good; is one, holy, catholic, and apostolic; the presence of sin not withstanding.