If you are unavailable and a client needs contact, a colleague’s contact information can be included. The text should also indicate when it’s appropriate to contact the alternate. Some people will indicate that the contact is for urgent matters while others may offer for consistent client care.
Also, you need to know your audience if you are going to go eccentric. Alison mentions that this message is fine in their culture, but it wouldn’t npbe appropriate for my somewhat formal field. And even if your workplace in general is casual, you might be contacted by someone outside. (In a tiny provincial courthouse I served in the past, there is a story going around that in the 80s a junior but elderly clerk used to address phone callers as hun and sweetheart and generally speak very informally. Most people thought it was funny, and then the President of Supreme Court called and… he didn’t).

Thank you for your e-mail. I will be on leave on 26th Jan with no access to email. I will revert to you on my return on 27th Jan.
About the “overshares”: You linked to a previous column that mentioned this point, “Sometimes the over-sharing of plans can even come across as suspect — similar to how when someone’s calling in sick with genuine illness, they usually just say, ‘I’m going to be out sick,’ but fakers will generally give you a long list of overly specific symptoms, like they feel they have to convince you.”