The easiest and most accessible way to manage the Cloud Security Connectors is to use AWS Systems Manager. AWS official documentation is available here: https://aws.amazon.com/systems-manager/.
The CSC has preinstalled the SSM Agent. You must register the CSC using "Hybrid Activations" and "Run Documents" afterwards.
With AWS Systems Manager, you can manage the CSC remotely. To do it, you need to create "Documents" in advance. "Documents" are a series of commands used by the "Run Command" functionality.
Attached to this article is the Cloudformation template to generate the "Documents" (commands)to remote manage the CSC PriCPA.