In Part Three, the hobos that Montag meets aren't really hobos at all; they are a group of men, mainly former college professors, who had to flee the city because they are wanted by the authorities. One man, for example, says that he hit a fireman who came to burn his books and has been running ever since.
These men identify as famous authors or pieces of literature because that explains and defines their new purpose. They are book covers: men who have memorized a book so that, one day, it might be written down again for a new generation to read. When Montag joins them, he becomes the Book of Ecclesiastes because he has committed the text of this book (or most of it) to memory.
These men are, therefore, waiting for society to break down so that they can step forward and help to rebuild. They want to create a new society in which book-reading and learning are not prohibited. For them, the future is the focus. This explains why Montag immediately joins them.