I'm looking for a good way to approach my manager that I believe his availability while on vacation sets a bad precedent for the team.
Some background. My manager is a People Manager of myself and my teammates. I'm a senior technical member of the team. Whenever he goes on vacation he's always available via company chat and email; he'll respond to email threads he's CC'd on, he'll obviously be paying attention to various chat channels and respond. I believe he means well and just wants to make sure things are under control and there are no blockers. While I can see how this can be viewed as him being "a manager going above and beyond" and "a good team player" etc I believe it is bad for two reasons: 1) he's not fully "unplugging"; I want him to come back from vacation fresh. 2) It sets a precedent to other team members that they're expected to be available when on vacation.
What I've tried so far: Whenever he's about to go on vacation I make sure to understand what projects need to be handled while he's gone and make sure that myself or someone else is on it. I also make it abundantly clear that we've got the situation under control and in the unlikely event of catastrophe we've got his phone number and will not hesitate to reach out.
Would it be best to approach him directly about this or would that be stepping on toes? ie, should I talk to his manager about it?