South African citizen to leave airport to see Great wall in a layover

The first and the most important detail is that your itinerary is eligible for 24 hour visa free transit and you do not need any kind of visa.

This scheme allows you to travel via China visa free, but exiting the airport is not an inherent passenger's right. However, Chinese authorities have decided on case by case logic to allow the so called temporary entry permits to those with long layover, to those with overnight layovers and to those who travel with small children. Your 14 hour layover is a long one and your chances to be granted a temporary entry permit are really very good.

In order to obtain a permit, you will immediately approach the transit counter upon your landing in Beijing. There you will apply for a permit by presenting your flight tickets that you should have in a hard copy for easier handling. This application is free of any charge. I expect with high degree of certainty that you will be granted a permit, but a warning, this is not guaranteed. If you plan to visit a Great wall and if you plan to visit it in an organized way, you will present your tour booking. This will even more increase your chances to be granted a permit.

In the end, the only 100% certain option that you will be allowed to exit the airport is a Chinese transit visa obtained in advance. However, if I were you I would take a chance and apply for a temporary entry permit upon landing in Beijing.