Not exactly what you are looking for, but I recommend 1491 by Charles C. Man. It gives a really fascinating look at several cultures within the Americas, particularly the natives in Peru. I read it on my trip to Peru and it enhanced the trip for me. I will note that some historians really disagree with some of the ideas put forward in the book.

It's not so much history and it's a bit silly at times, but Turn Right at Machu Picchu has some history of Peru throughout, though it isn't really in-depth and is written for a popular audience.

This might not be exactly what you want, but read River of Darkness by Buddy Levy. I don't know what you mean by true history. The main plot is about Francisco Orellana, an Explorer hoping to find a 3rd empire to exploit, after the Aztec and Inca had fallen. He ended up taking an accidental voyage in 1541/1542 from Ecuador up some rivers and down the Amazon. The politics of the Pizarro era in Peru and Ecuador are discussed. It's fascinating.