I'm very interested to read more about that Greek saying. Do you have a reference of it somewhere?
Wiktionary [2] refers to St. Jerome
> Proverbs 16:27 may have inspired St. Jerome to write in the late 4th century: fac et aliquid operis, ut semper te diabolus inveniat occupatum, or “engage in some occupation, so that the devil may always find you busy.” This was later repeated by Chaucer in the Canterbury Tales, which was probably the source of its popularity.
[1] https://naob.no/ordbok/lediggang
[2] https://en.m.wiktionary.org/wiki/idle_hands_are_the_devil%27...