“Red-eye gravy” was first called “red gravy” and then “red ham gravy.” Red gravy (from cured ham) was served through the South in the 19th century, in states such as Virginia and Georgia and Tennessee.
 
Some internet websites claim that U.S. President Andrew Jackson (1767-1845) named “red-eye gravy,” but “red-eye gravy” is first cited in a 1931 advertisement for the Milam Cafeterias in San Antonio, Texas. Subsequent 1930s citations for “red-eye gravy” all appear to be from Texas. The “red eye” term may come from the fat circles in the red-colored gravy.
   
     
Wikipedia: Red-eye gravy
Red-eye gravy is a thin sauce often seen in the cuisine of the Southern United States and associated with the country ham of that region. Other names for this sauce include poor man’s gravy, bird-eye gravy and red ham gravy. The gravy is made from the drippings of pan-fried country ham that has been mixed with water or black coffee. The same drippings, when mixed with flour, make the flavoring for a white gravy. Red-eye gravy is often served over ham, cornbread, grits, or biscuits.
 
A common practice is to dip the inner sides of a split biscuit into the gravy in order to add flavor and keep the biscuit from being too dry when a piece of country ham is added between the two halves: the Southern “ham biscuit.” Another popular way to serve red-eye gravy, especially in parts of Alabama, is with mustard or ketchup mixed in with the gravy. Biscuits are then “sopped” in the gravy.
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Origin
One folk legend surrounding the origin of the “red-eye” name credits former United States President Andrew Jackson with requesting ham with gravy as red as his cook’s eyes, which were bloodshot from drinking the night before.

Another circulating explanation is that the black coffee in the gravy will keep people awake. A more empirical account of the name’s origin is that “red-eye” describes the oily fat circles that appear in the gravy.
 
Preparation
The basic recipe for red-eye gravy is quite simple. Begin by pan-frying a fatty piece of ham. When the meat is cooked, remove it, and add water and/or black coffee to the pan along with sugar, which must still contain the ham grease. Bring the mixture to a boil, then simmer until reduced to the desired thickness, all the while stirring and scraping the pan so that the ham drippings dissolve in the gravy.
 
This Dog’ll Really Hunt:An Entertaining and Informative Texas Dictionary
by Wallace O. Chariton
Plano, TX: Republic of Texas Press
1999
Pg. 130:
Gravy, red eye: gravy made by mixing boiling water and strong black coffee with the juice from fried ham. The gravy is stirred until the liquid is well mixed with the juices and small pieces of ham that were left in the skillet. This delicacy was supposedly named by Andrew Jackson, when he remarked that the gravy looked like the “red eyes” of his cook, who had gotten very drunk the night before.
   
(Dictionary of American Regional English)
red-eye gravy n Also red-eye, red-eyed gravy, red-eye ham gravy.
A reddish, usu unthickened gravy made from the drippings of ham or other cured meat.
1945 SW Rev. 30.143 TN, Pinky brown slices of cured ham that almost floated in red-eye gravy.
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red gravy n
also red ham gravy, red sop; = red-eye gravy.
1939 Harris Purslane 302 eNC, We like them for breakfast with red ham gravy.
     
19 February 1887, Lowell (MA) Weekly Sun, pg. 6, col. 4:
There was old ham, the sort that makes red gravy, and fresh pork and turnips…
 
17 June 1894, Atlanta (GA) Constitution, pg. 10, col. 2:
Mrs. White, the good wife of the postmaster at Panthersville, gave us red ham gravy the day we dined with her, and this very gravy has been the keeping of us from getting off something nice about her clever treatment and splendid meal. Brown does the poetical work for this firm, and he declares that nothing but thoughts of that gravy trotted through his brain whenever he called up the muses. Gravy, gravy, gravy! Red gravy from Georgia raised meat, cured in the old-time way, is a subject that Brown cannot handle, nor can he collect the great variety of other things that were upon the table into a pretty poetical bouquet, because the red gravy will not down, but every time his thoughts confound—Brown is a monomaniac on red gravy.
 
19 May 1895, Atlanta (GA) Constitution, pg. 30, col. 2:
Smoke soon curls from the kitchen chimney, the squall of two or three frying chickens is heard for a moment before they lose their heads, the old smokehouse door swins back with a squeak, and visions of ham and red gravy fill your mind.

18 October 1903, Atlanta (GA) Constitution, pg. 4, col. 6 ad:
Jeremiah Murphy’s famous “Red Gravy” Hams, Monday and Tuesday, lb. ... 14c
       
30 October 1906, Galveston (TX) Daily News, pg.  10, col. 7 ad: 
Murphy Red Gravy Hams, something extra fine, every ham tagged “inspected,” per lb. ... 17c
   
28 March 1920, Washington Post, pg. 64:
[Quote by Senator Nat Dial of South Carolina—ed.]
“The man ‘who loves not the concord’ of hot hominy and good red ham gravy, or maybe chicken hash, is ‘fit for treasons, stratagems and spoils.’”
   
24 June 1921, Olean (NY) Times, pg. 6, col. 3:
RED GRAVY
If you would make red ham gravy sprinkle the ham with sugar before broiling. 
 
7 September 1921, Galveston (TX) Daily News, pg. 4, col. 3:
It might even be real red gravy of the kind that comes of frying real home-cured ham.
 
28 April 1931, San Antonio Light, pg. 10A, col. 7 ad:
Old Virginia
HAM STEAK
A thick, tender, flavory cut…fried in the pan…served with red-eye gravy and steamed rice.
25c
MILAM CAFETERIAS
 
14 February 1937, Abilene (TX) Morning Reporter-News, pg. 12, col. 1 ad:
DINNER..at the HILTON
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Fried Sugar Cured Ham Steak—Red Eye Gravy
 
15 April 1938, Brownsville (TX) Herald, pg. 2, col. 7 ad:
Ham Steak, Red Eye Gravy
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Blue Bonnet Cafe
 
5 March 1939, Port Arthur (TX) News, pg. 4, col. 7 ad:
Honey Cured Ham Steak, Red Eye Gravy
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Goodhue Hotel Coffee Shop