You need to preserve distinct indigenous elites, given that the liberation wars were driven by criollo elite demands for greater autonomy and power within the empire (similarly to the American Revolution) rather than any true drive for a broad liberal democracy. In most of Latin America, this is very difficult. However, I could see a surviving Inca elite falling under Spanish rule, with Andean indigenous languages widely spoken among the elite as well as Spanish. If Madrid suddenly ceased to have significant authority, I could see indigenous elites aiming to seize power and restore an independent monarchy updated with European governmental technologies.
This is OTL. The Inca nobility was of course, subordinated to the Spanish authorities, but it had a position of great prestige in the Viceroyaltly of Peru, with prominent Inca families holding much influence; they even had coats of arms and were included in paintings and ceremonies with important figures of the viceroyalty, together with Spanish nobles. In fact, most administration outside the cities was still conducted by 'Indian' authorities; native curacas or chiefs administrated many native comunities (and indigenous languages are still widely spoken today) that trasitioned mostly untouched from the old Inca Empire to the viceroyalty. As far as the Independence Wars, Manuel Belgrano in Argentina proposed crowning a descendant of the 'casta del chocolate', as they were called, as king of the United Provinces of La Plata, to legitimize it with foreign powers and the native Indian population (of course he was rejected).
In fact, a large reason of why the Incas and many other 'Indians' did not support the Independence Wars is that they feared the loss of their priviliges under the Spanish. There were many exceptions though. They were still subordinate to the Europeans, and as Tupac Amaru demostrated, they would have broken free if they could.
I am not as informed, but I think it was the same case with Aztec and other elites in Mexico. The other colonies like current Argentina had lower Indian populations without established elites. Paraguay is a case of its own.
I have some sources in Spanish about the perspectives of the Inca elite during the Tupac Amaru rebellion.
Yes, but it is proof that Indian populations were organized, large and had the will to lead a rebellion, and success, while unlikely, is not out of the question.