My company publishes >1,000 layers using several geoservers. We are publishing them on several different websites. Because there are so many layers, it is impossible for us to know which layer is being used and which one is not. Therefore, I was wondering whether it is possible to view the last time a layer in Geoserver was requested. Is there any option to know this?
The best possible solution for you is to check the logs for your webserver.
In our case, we are passing all our requests through Apache, which is functioning as a reverse proxy. We regularly look at Apache's Access Logs and see which of our services are most used, and act accordingly.
If your Geoserver is hosted in Tomcat, or Jetty, you can enable the access log in those webservers directly, and use those Access Logs. Unfortunetly I don't have much admin experience on these two webserver, so I would not be able to tell you how to enable logging.