Stop a mailbox syncing between 9am and 5pm
That sounds like a perfect job for tasker (see the tasker tag-wiki for some background). Example profile in "Pseudo-Code":


Condition: Time, start: 9am, end: 5pm
Task: Sync off
Exit-Task: Sync On


Notes:


"Exit-Task" is optional. If not defined, Tasker restores the state from before the Task started.
"Sync Off" applies to more than just mail (includes e.g. contacts, calendars, etc.). If you want to only pause mail sync, you need a mail app with Tasker support, e.g. K-9 Mail, maybe with some additional plugin. I know that's possible with K-9, and it's more than likely there are some other supported Email Apps. If using such a client, replace the "Sync off" / "Sync on" with the corresponding plugin action.