I wonder if there is any similar idioms to "When the cat's away, the mice will play." I searched on a few websites (the free dictionary, dictionary.com, and cambridge.) but there was no suggestions idioms.
Here are three tangentially related proverbs from Wolfgang Mieder, A Dictionary of American Proverbs (1992):
The cat is mighty dignified until the dog comes by.
It is easy to be brave from a safe distance.
Opportunity makes a thief.
Also somewhat related (in different ways) are these from Rosalind Fergusson, The Facts on File Dictionary of Proverbs (1983):
Make hay while the sun shines.
Gather ye rosebuds while ye may.
When fortune smiles, embrace her.
Hares may pull dead lions by the beard.
If the dog is not at home, he barks not.
The last item above is identified as an "African proverb."
Under its entry for phrases relating to absence, ‘New American Roget's College Thesaurus in Dictionary Form’ groups “Out of/outta sight, out of/outta mind” with “When the cat’s away, the mice will play.”
“Proverb: out of sight, out of mind 1. When something [the cat?] is not nearby, it is forgotten about.” (from Wiktionary)
In Sue Monk Kidd's "The Invention of Wings", the character Aunt-Sister says "Make hay while the mice away". In the context she means to tell the other slaves to keep busy with chores while the masters are away from the plantation. I don't know why it means that, except perhaps as a malapropism for "when the cat's away..."