I was curious of how the definition of Full Monty came to mean naked or nude so I checked Oxford dictionary for it’s origin. It seems as though the first mention of this phrase as meaning nude came from the film itself as it this is the earliest record that Oxford has for this meaning. The next to earliest record of this phrase came from 1985’s K. HOWARTH’s Sounds Gradely (North West Sound Archive) but the meaning here was everything included..a thorough display so there is a connection between nudity and thorough display.
Though this website: http://www.phrases.org.uk/meanings/full%20monty.html
theorizes that the earliest Full Monty derivation is from Montague Burton’s complete three piece suit sets. If this is true then it’s ironic that the phrase used for a full set of apparel came to eventually mean nakedness.