Rotate by day or by week
Give one person the queue for a day or a week and everyone else a break from it. Daily rotations suit high volume, and weekly ones suit low volume. Choose what keeps handovers few.
Write down the duty
State what being on duty means: check the inbox at set times, reply within your target, tag what you cannot solve and note anything you hand over. A shared page keeps everyone on the same rules.
Hand over properly
At the end of a shift, leave a short note with open tickets, anything promised to a customer and anything waiting on someone else. Five minutes of notes saves the next person an hour.
Plan for absences
Name a backup for each shift for holidays, sickness and meetings. Without one, a customer's message waits until someone happens to look.
Protect the off-duty people
Agree that people not on duty are not interrupted for routine tickets. They can help with a real emergency, and the rule is only fair if everyone sticks to it.
Look at the load
Once a month, check who handled how many tickets and how hard they were. Adjust the rotation if one person keeps getting the difficult days.