Don't email like a lab rat.
Like lab rats, we respond to triggers, develop habitual actions, and love rewards. Thankfully, as humans, we can also make our own triggers, develop habits consciously, and design our own rewards.
I appreciated the refresher course on these principles while watching the training videos for Prasanth Nair's Stack Method last week. Nair sees the fundamental problem as how we view emails. They're not just messages. We should view them as actions, invitations to reply, review, do, or meet.
If you value productivity over responsiveness, you have to choose a method for managing email. If you want to ensure you have time to devote your full attention to the relationships and tasks that really matter, turn off all notifications and process in batches. The time lost switching attention from writing a report to scanning the email alert that popped up to checking out the Instagram alert on your phone adds up to weeks every year (According to the American Psychological Association, "even brief mental blocks created by shifting between tasks can cost as much as 40 percent of someone's productive time.")
Having a process and choosing times to process email will make every aspect of your life richer. You may be inclined to discount what I'm saying because Nair invented his method in 2004, David Allen wrote Getting Things Done in 2001, and Merlin Mann gave this talk in 2007. But, before you do, spend 40 minutes watching Mann's classic Google Tech Talk and see if you can find any principles espoused there that don't still hold water. If. nothing else, have a few laughs.
Then get back to your email overlords!