Gospel of Saint John Chapter 6 verses 66 through 70
66 And he said: Therefore did I say to you, that no man can come to me, unless it be given him by my Father. 67 After this many of his disciples went back; and walked no more with him. 68 Then Jesus said to the twelve: Will you also go away? 69 And Simon Peter answered him: Lord, to whom shall we go? thou hast the words of eternal life. 70 And we have believed and have known, that thou art the Christ, the Son of God.
The whole game of Apostate Babylon presenting the "Universal earthly head over the non-church."
"So, sedevacantists do not even reject the pope, but profess they need one and want one. This means with "greater reason" their consecrations are recognized as valid."
That is the whole game of Apostate Babylon, both traditionalist recognize and resist (i.e. SSPX) and the Sedevacantist (there is no valid Pope since the Apostate Antipope John XXIII, but we have to have one) in regard to presenting the "Universal earthly head over the non-church."