Testing an HA solution is a time consuming process, with many variables. This is particularly true considering a cross-platform application. You need a trained system administrator or a consultant to do this work. It is not something we can cover in depth in the documentation.
That said, here are some pieces of your infrastructure you should be sure to test:
One thing that you should not do is run kill -9 on a postmaster process. This is because doing so does not mimic any real life scenario. If you are concerned your infrastructure is insecure and an attacker could run kill -9, no amount of HA process is going to fix that. The attacker will simply kill the process again, or cause chaos in another way.