usually with Queue’s you give the waiting caller the ability to press 1 (or any other number) to leave a message for the agents. This then leaves a voicemail which you can use the voicemail to email functionality to provide what you are asking for.
- create an IVR with that has an option to leave a voicemail if a certain number is pressed
- create an announcement that says something like “We’re sorry to keep you waiting, if you’d prefer to leave a voicemail and have someone call you back, please press 1 now or continue to hold for the next available agent” and that then transfers the call to the IVR you just created
- Applications > Queue > Call Announcements > IVR Break out menu
Place the announcement there and select how often you would like the caller to hear this option. I usually put 5 minutes but it depends on how busy the queue is in your particular situation.
There may be a better way to do it but that’s what I know.