Though in terms of Shakespeare, my favorite bit on keeping quiet is actually Iago's last line: "Demand me nothing: what you know, you know:
From this time forth I never will speak word." My wife and I tend to quote it around Christmas and birthdays. :-)
Various English posters and signs in WWII warned readers to 'be like dad – keep mum'.
https://upload.wikimedia.org/wikipedia/commons/3/3e/INF3-243...
https://www.gettyimages.com/detail/news-photo/be-like-dad-ke...