Is it an absolute requirement that the Pope be a Bishop of Rome?

And would he have to have a "Preexisting" connection to the diocese?

I know there were a couple of "competing papal claimants" in history, but I forget if the true Pope was always in Rome or not.

At any rate I guess my issue is, were at 62 years and counting now (per sedes) so I don't see how the sede argument seems to be "well Francis isn't the Pope, but also, the True Church has no way of giving itself a pope."

I guess the issue is further complicated if you take an SSPV style opinionism, in which case, most True Catholics do think Francis is the Pope, even if some of the SSPV priests think he isn't.  That makes things even more complex and weird.

Not necessarily.  That was cleared up later by the Church, of course, but it would have been theoretically possible that none of them had been legitimate ... for different reasons.  Evidently the group that elected the first anti-Pope felt that the original election had been illegitimate.

In theory, there's nothing preventing it.  Bellarmine addresses a scenario where all the Cardinals would be killed.  He simply states the principle that the Church has the power by Divine Law to select a Pope, and that the institution of Cardinals is man-made.  He stated that if the Cardinals would die, then the authority would be upon the clergy of Rome, but if they had died too, then an Imperfect Council could elect a pope.

Problem is that there also has to be Universal Acceptance that the process is legit.  If 10 sedevacantists got together here, and 20 over there, and no one agreed, then there's nothing that constitutes a selection of a leader by THE CHURCH ... just little groups.  And even if all the sedevacantists got together and elected someone, then you have the sedeprivationists who would not accept it, nor the R&R, nor those Catholics who remained in the Novus Ordo.  So, given the fragmentation of this crisis, it's a practical impossibility that such an election would be legitimate (assuming, for the sake or argument, that the See IS in fact vacant ... since, if is not, then the answer is clear).

So that's why Bellarmine stated that the authority would devolve in the last resort to an Imperfect Council ... because there has to be SOME notion of universality and Universal Acceptance of the process and its results.

When some sedevacantist groups have gone off and elected popes, it had to be with the at-least-implicit notion that they were the only Catholics left, that those who didn't agree with their election were no longer Catholics, and that certainly those who were not sedevacantists were not Catholics.  Thereby, in eliminating all these people from the Church, there would remain a "universality" among the Church, since the Church would effectively be reduced to those who accepted the "Pope".  So it ends up being a bit of a tautology, and the corollary of conclavism is the notion that they who elected the Pope are in fact all that remains of the Church.

I get that all these conclave groups are illegitimate, because they don't *even* entail a unity of those who do not think Francis is the Pope.  That the Sedevacantists still cannot gather together and elect in unison a new pope, heavily inclines me to believe that the real reason that they can't is because we have a Pope, just a very bad one.