Not exactly what you are describing as its more of a callnot answered situation thatn an operator idle one
Class of service / Advanced /Attendant
Attendant Busy Out Timer
This timer defines the length of time in minutes for which calls will be queued at all attendant consoles before switching the console to Absent mode (busy out).
Enter a value from 1 to 1440, where an entry of 1440 will turn off the Attendant Busy Out timer.
Entering "1440" for Attendant Busy Out Timer disables the feature for that COS.
If I never did anything I'd never done before , I'd never do anything.....