When it begins in earnest and for the last time, it will be universal. There won't be an effort among one part of the vineyard which isn't mirrored by similar efforts in other parts of the vineyard. All the natural branches will be returned and reunited with the natural roots, as all are gathered again into one.
The Father will determine the timing. The Son will implement the plan. The process will require everyone, in every scattered part of the vineyard, to "come unto Christ." Unless they "come unto Christ," they will not be gathered and cannot be saved.
What does it mean to now call all those who are to be included in this final gathering "his people" meaning the Father's people? Why would they end their long sojourn by becoming the "Father's people?" Christ has spoken of them being "His people" (meaning Christ's) but now the culmination will result in them becoming the "Father's people" as well. (D&C 76: 92-95.)
There will be gatherings, and a great gathering, and at last a distribution of the survivors into their respective promised lands. Between the time of the great upheavals, and the time of the final distribution, there will be a season in which there will a great gathering in the "Mountains" (2 Ne. 12: 2) where it will be a fearsome, even terrible thing for the wicked to contemplate. (D&C 45: 68-70.) This will be in "the tops of the mountains." (Micah 4: 1; 2 Ne. 12: 2; Isa. 2: 2.) This will be where the New Jerusalem will exist. This will be before the final distribution into the various places of inheritance of the Lord's people.
The choice is between the Lord, His offered redemption and protection, and destruction. The gentiles are now offered a choice while reenacting the same poor judgment that led to their own loss of opportunity. That needn't be true of individuals. It seems apparent that the prophetic message of the Book of Mormon foretells gentile arrogance and pride, collectively claiming they are on the road to Zion, while they are instead doomed to repeating the errors of prior civilizations of this continent. We will get to that in the coming days, but for now we remain interested in the definition and destiny of the "remnant" of the prior occupants.
(What an interesting text this Book of Mormon proves to be. It makes one wonder why it would ever suffer from neglect.)