The first time we were required to show an Exit Ticket or Proof of Onward Travel was at OR Tambo Airport. We were checking in to leave on our epic adventure to travel the world full-time.
We bought a one-way ticket to Brazil, the cheapest we could find at the time. We didn't have any set plans, no time limit, no nothing. Now the airline (SAA) wanted us to have a ticket back to South Africa! Not even an onward ticket. What? We were so worried. We can't even leave South Africa!
We did kind of know that this might be the situation. And this is mostly enforced by airlines because they will have to send you back to your country of origin at their cost if you are not permitted to enter the said country. Since they are liable, they can refuse boarding of passengers who don't have a return ticket.
Luckily, I read about two websites prior to leaving where you can basically book a flight without paying - they keep the ticket "on hold" for a certain amount of time. Just enough for you to prove that you have a return ticket.
So how do you get a ticket without paying? Many people create false tickets or some pay about $20 just for proof of a ticket without paying for an actual ticket. Obviously, it is better if you can actually book a flight to another country if you know where you are going next.
Step 1: Go to the following website: www.yatra.com
Choose your "from" city and destination city in the next country. In the example below, we chose to "fly" from Buenos Aires back to Johannesburg. Choose the date within your allowed amount of days in the country. Click Search.

Step 2: Your search results will come up. Look for the "hold for free" button. Sometimes, you have to scroll all the way down to the bottom of the results. Sometimes, there is no results available to "hold for free". Just choose another search and try again until you succeed.

As can see in this example, you can also cancel this booking for free on the same day. It doesn't really matter because you won't pay, but if you have this option without the hold for free option and can cancel within a day, you can also do that.