Is the concept of the 'Axial Age' a construct of modern thinkers or is it based in reality?
First, all periodization of time periods in the past are categories created by scholars at some point. In the 19th and early 20th centuries, historians were particularly keen on "ordering" the past -- partially as a result of positivism (Auguste Comte, etc.) and the push towards an empirically defined world that agreed with ideas of empirically based science popularized by Darwin and company. The so-called "Axial Age" is a product of this, as is the Middle Ages, the Renaissance, Orientalism, and Western Civilizations (thought the history of the former two is quite a bit longer). What modern historians have come to realize is that placing strictures such as these onto the past oftentimes prevents people from recognizing that history is not broken up into nice, neat chunks that are independent of each other. One period did not simply end and another begin with a new set of ideas and goals, neither does a particular region stop at an imaginary border. The most important thing to understand is that history involves change over time -- sometimes that change is fast, sometime it is slow; sometimes it involves only a few people, sometimes many people; sometimes it moves from place to place, sometimes it stays put; sometimes it is viewed as good, sometimes as bad. Whatever the case, stuff changed, and it is the historian's job to investigate that change in whatever form it took and make some type of conclusion about it.
It is often easier (and usually more academically responsible) for a historian to consciously restrict their sources, time period, and other research parameters in order to make a valid conclusion about whatever they are investigating. Thus, particular sets of parameters (the Middle Ages, the Axial Age, the Middle East, or Colonial America, etc.) first became common in academia because of their utility, then made their way into the public where they were isolated and their broader context often ignored - which I don't think was ever the intention of chronologic periodization.
Here are some books that may help.
Marc Bloch. The Historian's Craft
James M Banner. Being a historian : an introduction to the professional world of history
3.Ernst Breisach. Historiography : ancient, medieval, & modern
Georg G Iggers. Historiography in the twentieth century : from scientific objectivity to the postmodern challenge
Edward Said. Orientalism
Hope this helps a little. Happy Reading!
Edit: Something funky with the list of books, apologies.