“A drunk(en) man’s words are a sober man’s thoughts” is a proverb usually listed without a source. “What is on a sober man’s mind is on a drunken man’s tongue” was listed in a 1941 book on Russian proverbs. “A drunk man’s words are a sober man’s thoughts” was listed as an Italian proverb in The Routledge Book of World Proverbs (2006).
 
The original proverb was recorded by the Greek essayist Plutarch (46 - 120 A.D.) in Moralia, “On Talkativeness”:
 
“For what is in a man’s heart when he is sober is on his tongue when he is drunk, as those who are given to proverbs say.”
 
“The drunken man speaks the sober man’s thoughts” was said by an American newspaper in 1868 to be a common saying.
   
   
Wikipedia: Plutarch
Plutarch (/ˈpluːtɑːk/; Greek: Πλούταρχος, Ploútarkhos, Koine Greek: [plŭːtarkʰos]) then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus (Μέστριος Πλούταρχος), c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia. He was born to a prominent family in Chaeronea, Boeotia, a town about twenty miles east of Delphi.
 
De garrulitate by Plutarch
as published in Vol. VI of the Loeb Classical Library edition, 1939
Plutarch, Moralia
On Talkativeness
Pg. 406:
For what is in a man’s heart when he is sober is on his tongue when he is drunk, as those who are given to proverbs say.
   
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April 1772, The Oxford Magazine, “On Drunkenness,” pg. 128:
Those things which are hid in a sober man’s heart are oft-times revealed by the tongue of a drunkard.
 
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The Gull’s Hornbook, or fashions to please all sorts of gulls
By T. Decker
Bristol: J. M. Gutch
1812
(The Guls Horne-Booke was originally published by Thomas Dekker in 1609, but this appears in a note apparently written by John Nott—ed.)
Pg. 22:
Treatise on Garrulity: Those who deal in proverbs say; that what is in the sober man’s heart, is on the drunkard’s tongue. hence Bias, sitting silent at a banquet, and being upbraided with stupidity by a talkative coxcomb, replied: “Where is the fool that can be silent in his cups?” This anecdote is very neatly narrated in John Lyly’s Ephaebus, subjoined to his Euphues.
 
It may not be improper to remark in this place, that many of the apothegms of the wise Grecians were borrowed from the Jewish writers; the foregoing from Plutarch may be traced in Ecclesiasticus, Chap. 21, Ver. 26: “The heart of fools is in their mouth; but the mouth of the wise is in their heart.”
 
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Mental Recreation, or,
Select maxims, sayings, and observations of philosophers, statesmen, divines, and other great men, ancient and modern: upon most subjects
London: Printed for Longman, Rees, Orme, Brown, and Green
1831
Pg. 70:
“Those things which are hid in a sober man’s heart, are too often revealed by the tongue of the drunkard.”
 
6 August 1868, The Daily Bulletin (Leavenworth, KS), pg. 4, col. 3:
It is a common saying that the drunken man speaks the sober man’s thoughts, and it is probably that this fellow is either one of the murderers or a brute more cowardly, who joined in that terrible brutality.
 
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Selected Essays of Plutarch
Edited by T. G. Tucker
Oxford: Clarendon Press
1913
Pg. 133:
As the proverb-makers put it, ‘What is in the sober man’s heart is on the drunken man’s tongue.’
 
7 February 1932, Sunday World-Herald (Omaha, NE), “‘Best Mixer’ Is Still for the Dry Law,” Magazine Section, pg. 6, col. 6:
“There was an old saying that ‘A drunken man speaks a sober man’s mind,’ and there’s a lot in that.”
     
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The Spoken Word
Volume 3, Issues 1-20
1936
Pg. 18:
You have often heard the saying which is quite often used in America and also in other countries: “A drunken man speaks a sober man’s thoughts.”
 
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The New Day
Volume 1, Issues 23-41
1937
Pg. VI:
Such is the fulfillment of the saying that “A drunken man speaks a sober man’s mind.”
 
Google Books
Certain aspects of Russian Proverbs
By Andrew Guershoon
London: Muller
1941
Pg. 158:
What is on a sober man’s mind is on a drunken man’s tongue.
 
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Famous Judges and Their Trials:
A century of justice
By Leonard R. Gribble
London: J. Long
1957
Pg. 17:
And once, for no apparent reason except possibly that a drunken man speaks a sober man’s thoughts, he snapped at the lodger: ...
 
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The Key to My Prison
By Harris Downey
New York, NY: Distributed by Dial Press
1965, ©1964
Pg. 115:
There’s a saying that a drunk man speaks a sober man’s thoughts.
   
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Hieronymus Bosch and the Canticle of Isaiah
By Marshall Neal Myers and Wayne R. Dynes
New York, NY: Cabirion Press
1987
Pg. 53:
“A drunk man’s words are a sober man’s thoughts,” says the proverb, and this well describes how comments usually kept quietly in check can escape to wreck havoc through the agency of strong drink.
 
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Russian Culture at the Crossroads:
Paradoxes of Postcommunist Consciousness
By Dmitrij N. Šalin
Boulder, CO: Westview Press
1996
Pg. 211:
Which is why it is said, “What is on a sober man’s mind is on the drunkard’s tongue.”
   
Google Books
The Routledge Book of World Proverbs
By Jon R. Stone
Abingdon, Oxon: Routledge
2006
Pg. 117:
A drunk man’s words are a sober man’s thoughts. (Italian)
   
Google Books
Wise Quotes of Wisdom:
A Lifetime Collection of Quotes, Sayings, Philosophies, Viewpoints and Thoughts
By R.A. Wise
Bloomington, IN: AuthorHouse
2011
Pg. 4:
A drunk man’s words are a sober man’s thoughts. proverb
 
Google Books
Duped!:
Delusion, Denial, and the End of the American Dream
By Jerry Kroth
2012
Pg. ?:
There is a Russian expression: “What is on a sober man’s mind is on a drunken man’s tongue.”