If you are in a position to know that the agent is truly available to take calls then you are in a position to tell them to become available. In just about any business this is called "managing".
Depending on your age, this is probably something your father dealt with in his job from either one side or the other. If you are fortunate enough to be able to seek his counsel you might want to do so to find out how it worked, how it felt and most importantly what the result was.
CMS provides tons of information that can be used to monitor and report on agent behavior. As important as after the fact reporting is, it is equally important to establish performance criteria, communicate it to the employees and then use reporting to ensure that the employees are in compliance. And when they are not it is incumbent on the manager to deal with the issue promptly, reasonably and forthrightly.
If I have misunderstood your issue or over reacted I apologize but it trips my trigger when people want technological solutions to management problems.