The rule: Never expect, or demand, immediate replies.
Avoid using the words "Urgent!" or "Emergency!" in email titles. Truly urgent matters should be communicated over the phone: Nobody emails 911 when their house is on fire – they call.
Instead, mark time-sensitive emails as such and calmly explain your reasoning and the target date for a response. Then, allow a few days for your recipient to process the information. If you feel like your email might have been overlooked and a reminder is necessary, consider using other channels of communication like a text message or phone call.
Understand that the recipient might disagree with your assessment, and while you may believe your issue should be at the top of their to-do list, they might be busy saving the world from an incoming asteroid threatening to wipe out humanity.
Or, they had to grab some lunch.
Key takeaway: Respect others’ time. Your emergency is not necessarily their emergency, and they’re just as busy as you are.