Is it possible to configure the Send on Save option so it sends response to customer at set time

Summary

We have agents responding to incidents outside of business hours and want see if it is possible for the response to the customer happens at the start of the next business day

Content

Effectively we are after something that works like the scheduled text function on your phone.  i.e set the time you want the response to be sent to the customer and close/save the incident. I was wondering if anyone has attempted or created anything that will deliver this type of functionality within Service Cloud. We believe it is possible with customizations, but I thought it may be worth learning from the collective experiences.