What web apps are available to dynamically forward email according to a schedule?

With increased remote working due to the pandemic, I’m looking for a better way of managing our support rota.

My use case is that we have people scheduled to take 3-hour shifts looking after an inbox. Currently it’s easy to forget to check, as it’s just a shared mailbox. I could turn it into a group, but we don’t really want everyone bombarded with emails when it’s not their shift.

Ideally, what I’d like is an email address to which I can set up an auto-forward, for it to then be forwarded on again based on a schedule/rota.

Does anything like this exist?