The interface between the two systems for this type of communication is the ARM (Agent Reporting and Monitoring) interface - the Listener on the CIM side, and the CTI server (e.g. CG1A) on the ICM side.
Set up trace on the CTI server and be sure that clicking the available/not available is changing state through the CTI server.
Agent availablility in the Router comes from your Agent PG. If the Agent PG does not inform the Router that the agent is not available, the router will give them another activity.
Regards,
Geoff