“Eat when you’re hungry” is an old saying and has been cited in print since at least 1841. In the 1880s, former Chicago mayor “Long John” Wentworth (1815-1888) said: “Now, my doctrine is this, eat when you’re hungry, drink when you’re thirsty, sleep when you’re sleepy, and get up when you’re ready.”
   
“‘Sleep until you’re hungry, then eat ‘till you’re sleepy’ (Navy JO Motto)” has been cited in print since 2005. “Sleep ’til you’re hungry, eat ’til you’re sleepy. ~ Author Unknown” has been cited since 2007.
   
   
Quotations about Food
Sleep ‘til you’re hungry, eat ‘til you’re sleepy.  ~Author Unknown
   
Wikipedia: John Wentworth (Illinois)
“Long” John Wentworth (March 5, 1815 – October 16, 1888) was the editor of the Chicago Democrat, a two-term mayor of Chicago, and a six-term member of the United States House of Representatives.
       
Google Books
Discourse on the enlarged & pendulous belly;
Shewing it to be a visceral affection, and attended with many important consequences in the human economy; with cursory observations on diet, exercise, and the general management of health, for the use of the dyspeptic.
By Richard Frankum
London: Longman, Orme, Brown, Green, & Longmans
1841        
Pg. 68:
Our own homely proverb, although we are not able to boast of acting upon such hereditary wisdom, is far more to the purpose:
   
Eat when you’re hungry, and drink when a-dry.
 
Chronicling America
11 February 1880, Louisiana Democrat (Alexandria, LA), pg. 2, col. 2:
“EAT when you’re hungry and drink when you’re dry,” is the advice of one of the DEMOCRAT’s staunchest friends, who died happy at a ripe old age.
   
Chronicling America
31 May 1883, Wichita (KS) Eagle, pg. 1, col. 9:
Natural philosophy—Eating when you’re hungry.—Philadelphia Chronicle.
 
Google Books
The cave of Hegobar:
or, The fiend of 1878. A story
By Robert Hoskins Crozier and Ellen B. Constant
Asbury Park, NJ: Presbyterian Pub. Co.
1885
Pg. 233:
“My general rule is to comply with the demands of nature — eat when you’re hungry, drink when you’re dry, and sleep when you’re sleepy.”
 
Google News Archive
30 April 1886, Crawfordsville (IN) Daily Argus News, pg. 4, col. 4:
AN EX-MAYOR’S DIET.
HON. JOHN WENTWORTH, OF CHICAGO LECTURES ON HYGIENE.
“Long John’s” Lease of Life—“Eat When You’re Hungry, Drink When Your (sic) Thirsty, Sleep When Sleepy”—A Brief Discourse on Drinks—Baths.
(...)
MEALS WHEN YOU WANT THEM.
He said: “I never was one of your bell-livers, I never did and never will live on time. Got no use for call-bells, dinner-bells, or alarm clocks, and I believe they do more for the general slaying of health and killing of people than either guottony or intemperance. Now, my doctrine is this, eat when you’re hungry, drink when you’re thirsty, sleep when you’re sleepy, and get up when you’re ready.”
 
Google Books
The Long Roll
By Mary Johnston
Boston, MA: Houghton Mifflin Co.
1911
Pg. 297:
“Gawd! Jest to drink when you’re thirsty, and eat when you’re hungry, and sleep when you’re sleepy — “
   
Google Books
Chicago Giant:
A biography of “Long John” Wentworth
By Don Edward Fehrenbacher
Madison, WI: The American History Research Center
1957
Pg. 228:
“My doctrine is this, eat when you’re hungry, drink when you’re thirsty, sleep when you’re sleepy, and get up when you’re ready.”
 
CarKB 
electron pimp - 17 Apr 2005 20:32 GMT
(...)
“Sleep until you’re hungry, then eat ‘till you’re sleepy” (Navy JO Motto)
 
Bus Conversions Magazine Bulletin Board
larryc
Re: New Feature for Bus Conversions Magazine
« Reply #7 on: November 13, 2007, 02:52:47 PM »
(...)
Sleep ‘til you’re hungry, eat ‘til you’re sleepy.  ~Author Unknown
 
Google Books
Rock-a-Bye Baby:
200 Ways to Help Baby (and You!) Sleep Better
By Penny Warner
San Francisco, CA: Chronicle Books
2008
Pg. 31:
“Sleep ‘til you’re hungry, eat ‘til you’re sleepy.” — author unknown
     
ieatishootipost
liverpool
Re: Fish Soup
Reply #9 on Apr 17, 2008, 10:00pm
Sleep ‘til you’re hungry, eat ‘til you’re sleepy.
 
Dr. Tom’s HipHappy Times
Food Creates Both Comfort and Confusion
Posted by Dr. Tom on May 22, 2008
(...) 
Sleep ’til you’re hungry, eat ’til you’re sleepy. ~ Author Unknown
   
20 June 2008, SunHerald (Biloxi-Gulfport, MS), pg. H1:
Nearby and above the windows a charming and agreeable saying is stenciled on the walls: “Sleep until you’re hungry, eat until you’re sleepy.”
 
New York (NY) Daily News
The sleep of a laboring man is sweet
Updated Friday, June 26th 2009, 4:36 PM
(...)
Sleep ‘til you’re hungry, eat ‘til you’re sleepy. 
Unknown