I used to work with someone who had a message telling people she only checked her email twice a day. You pretty much needed to call her if you needed anything outside of those times. (She worked in a remote office.) I think she had read one of those books on efficiency that recommended scheduled email time. But there were problems with this: 4. My department often had to email attachments or text to illustrate our questions/concerns. And we were on deadlines. Reading a page of text over the phone was not an efficient use of anyone’s time 5. She did outreach & was often out of the office on site visits, trainings, or travel to these places, but never ever set her OOO for these, because she was “working.” However, she was effectively not available to read emails from other staff until after hours on those days.
One of your European connections here. When I know the person covering me will also be away for part of the time I’m gone, I get another colleague to cover for those dates and put that in my OOO. Saying “Your e-mail will not be read” or similar is really off-putting. The youth worker at my church does this and I find it infuriating. Of course it won’t. That’s the point of a holiday. When I get an answer from someone who reads his e-mails on vacation I’m pleasantly surprised.

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Entrepreneurs and salespeople probably laugh at the prospect of being "out of office" — or, at the very least, unavailable to their clients 24/7. But the thing is, no one can be in the office 100% of the time. Even if your "office" is as portable as your laptop.