I am not a theologist, and I only met one Sedevacationist in an internet forum and he didn't seem quite sane to me, so I don't know how much his opinions are official. He said something like "the Pope has implicitly excommunicated himself by..." I don't remember what exactly was the reason, but probably because of the alleged heresy.

(Makes some sense to me. I mean, if you are serious about a religion and serious about the religious hierarchy, because you believe that the bishops are literally the messengers of God and the whole Church is the God's living body on Earth, or something like this, then... being a heretic, not being a Pope, but still pretending to be a Pope... that seems like an insanely serious offence. It's a religious equivalent of falsely pretending to be a King.)