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.
If you want to send multiple messages over different days, make sure each one includes all the information above so there aren’t any questions left unanswered. And remember — no matter how much space you give these notes, you still need to leave enough room for actual emails!

Given free rein, I’d absolutely love to tell people that needing me to show them how to do X in Excel is actually not a vacation-interrupting emergency and there are tons of free videos that would explain that, if they did not want to contact the actual departments who handle tech support and training. Or that this project they’ve known about for a month but decided to keep under their hat until it became an emergency is something they’ll need to resolve themselves. But that would not fly at all.
Pro tip: The first works well for both voicemail greetings and email responders, while the next two are most appropriate for emails.