Having taken the characters from the first part to a god forsaken town in Mexico the second part expands on one of the minor characters who lives there.
I use the expression minor because in the first part the Chilean philosophy professor Amalfitano is described in more detail. The academic is also plagued by dreams and starts hearing voices. Like the others he is also trapped not by his obsession with a reclusive author, but by his inability to leave somewhere he hates living in.
In one sense you see the second part a bit like a spoke on a bike wheel, adding more of the picture before it moves into the middle. Because in terms of story development it is hard to see where this is now going.
More when I have read the third part...