Better yet, tell your boss (and everyone else) you check for texts twice a day, and emails once a day, and respond with similar timeframes. If it's urgent, well, they know where you are. They can come and see you.
They'll whinge at you for living in the 20th Century, but your stress levels will be down.
Embrace the fact that no-one is irreplaceable, and train your understudies.
If I'm on vacation, I'll tell my boss I'm on vacation. Maybe I'll skim work emails and even handle ones when I can do so quickly but I'm under no obligation to do so.
They'll whinge at you for living in the 20th Century, but your stress levels will be down.
Embrace the fact that no-one is irreplaceable, and train your understudies.