Using email copy creatively can go miles when using an autoresponder. The mundane, repetitive language is the number one reason behind people sighing and not the unavailability of the concerned person. Getting creative with the email copy can de-escalate the frustration and even put a smile on their face. Everyone needs a break, and words can convey it beautifully like this example.
Not just that, but some e-mail systems (Gmail comes to mind) have taken to hiding the signature underneath a little expando-button. You don’t see it unless you go looking.

Thank you again for being the best team one could ask for. Your energy and persistence has driven our company to new heights, and we greatly appreciate it.
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.