About the definition of ketogenic amino acid
The fundamental 'problem' with acetyl-CoA is that it cannot be converted to glucose via the tricarboxylic acid (TCA) cycle: a two-carbon compound (acetyl-CoA) enters the TCA cycle, but two carbons are lost as CO$_2$ during each round of the cycle (in the two decarboxylation steps, ie in the reactions catalyzed by isocitrate dehydrogenase and by the alpha-ketoglutarate dehydrogenase complex). 

There is no 'net gain' of carbon when acetyl-CoA is 'burned' in the TCA cycle. 

This is why animals cannot convert even-number fatty acids (even-chain fatty acids) to glucose, and a basic principle of animal nutrition is that triglycerides, with the exception of the glycerol backbone, cannot be converted to glucose. 

This, is seems to me, is also the key to understanding the difference between 'ketogenic' and 'glucogenic' amino acids. 

Amino acids that directly give rise to acetyl-CoA (or acetoacetyl-CoA) cannot be converted to glucose but that can be converted to ketone bodies (such as D-3-hydroxybutyrate)  are referred to as ketogenic amino acids.

Pyruvate can be converted to glucose (via glucneogenesis), and amino acids that may be converted to pyruvate are considered glucogenic. A very good example is alanine which may be converted to pyruvate simply by transamination (alanine aminotransferase).

Alanine is a key protein-derived glucose precursor, especially in times of starvation (Felig, 1975). A commentary on the discovery of this key finding is given in this citation classic

In addition, amino acids that may be converted to TCA intermediates that in turn may be converted to phosphoenolpyruvate (and are thus precursors of glucose) are considered glucogenic (Lehninger, Biochemistry, 2nd Ed, 1975, p629).

We need to be aware that propionate (a three-carbon compound) is glucogenic (and this is particularly important in ruminants): it is even-chain fatty acids (and their CoA derivatives) that are non-glucogenic. 

Furthermore, an amino acid may be both ketogenic and glucogenic.


Only leucine and lysine (LK) are exclusively ketogenic 
Tryptophan, Isoleucine, Phenylalanine, and Tyrosine (WIFY) are both glucogenic and ketogenic 
The other 14 'protein' amino acids are glucogenic 


See  D'Mello (2003) for a great ref (it must be good, he's from Scotland). 

The catabolism of the branched-chain amino acids (Ile, Leu, Val) provide an example of each type (Harper et al., 1984): 


The catabolism of isoleucine gives rise propionyl-CoA and acetyl-CoA and is both glucogenic and ketogenic. 
Leucine catabolism yields acetoacetate and acetyl-CoA (ketogenic)
Valine catabolism yields succinyl-CoA (glucogenic)


A quote from Metzler (2001) may help to clarify the origin of the terms. 


  According to a long-used classification amino acids are ketogenic if (like leucine) they are converted to acetyl-CoA (or acetyl-CoA and acetoacetate). 
  
  When fed to a starved animal, ketogenic amino acids cause an increased concentration of acetoacetate and other ketone bodies in the blood and urine.
  
  On the other hand, glucogenic amino acids such as valine, when fed to a starved animal, promote the synthesis of glycogen 
  
  ... isoleucine is both ketogenic and glucogenic, a fact that was known long before the pathway of metabolism was worked out. 


Thus, in feeding experiments, a glucogenic amino acid gives rise 
to the synthesis of glycogen, whereas a ketogenic amino acid does not
(but does give rise to an increase in the concentration of ketone bodies)`


We may note that plants can circumvent 'the acetyl-CoA problem' as they have the enzymes of the glyoxylate cycle, where the two decarboxylation steps of the TCA cycle are 'bypassed' (the key enzymes are malate synthase and isocitrate lyase) [and plants can convert acetyl-CoA to glucose].

It is also of interest, maybe, that both arginine and taurine (not one of the 20, of course) are essential in cats (see D'Mello, 2003). Arginine is required because of an inability to synthesis ornithine and a single Arg-free meal may cause a cat to become comatose due to the build-up of NH$_3$ (see D'Mello, 2003; Bequette, 2003) , and taurine is required to prevent retinal degeneration (see D'Mello, 2003; Bequette,2003). In addition, cats need high levels of Phe/Tyr for melanin biosynthesis, otherwise hair color may change from black to red-brown (see Bequette, 2003)

Reference

Some key references given above are from the following book:

Amino Acids in Animal Nutrition (2003) Edited by J.P.F. Mello, CABI Publishing, 2nd Edition


D'Mello, J.P.F (2003) Amino Acids as Multifunctional Molecules by J.P.F. D'Mello (Chapter 1)
List Bequette, B.J. (2003) Amino Acid Metabolism in Animals:an Overview (Chapter 4) 


In Addition (Taurine in Cats) 


Carnivores Herbivores and Omnivores in Blondes in Venetian Paintings, the Nine-Banded Armadillo, and Other Essays in Biochemistry by Konrad Bloch