Under the rule wizard, the “After message has been received” only has two options, received and sent. Can a rule be created so that the email will be moved and filed “After message has been read”?
No, because a Rule acts only on messages as they pass between the server and client. Or in the case of IMAP when they enter the Inbox.
So either send or receive.
I used a program called Auto-mate with Outlook. It had a feature that would run rules after a certain amount of time. So I had it set to run the rules every 3 hours and it would go through and clean up my inbox if the email had been read. Is there a way to suggest that as a feature or is there a way to do this?
It is not possible to schedule Rules to run at specific times. They run automatically as new emails pass between the server and client. But a Rule can be run manually at any other time by right-click on the folder and choosing Apply Rule. The problem with your requirement is that the read/unread condition is not an available option.
You can propose ideas for consideration in future versions. Start a new topic in the same way as you created this question, but instead of Question you choose Idea.