Below are all the definitions of "Brilliance" that we could find. Secondly we consider why so many definitions exist followed by two definitions of "Brilliance" that match our understanding of this phenomenon.
We would be grateful if you will share your considerations, concerns and comments.

Definitions of "Brilliance":

From Tolkowsky's "Diamond Design", 1919:

The brilliancy or, as it is sometimes termed, the " fire " or the " life " of a gem thus depends entirely upon the play of light in the gem, upon the path of rays of light in the gem. If a gem is so cut or designed that every ray of light passing into it follows the best path possible for producing pleasing effects upon the eye, then the gem is perfectly cut.

Diamonds, E. Bruton (1978):

Eric Bruton F.G.A gives in his book "Diamonds" (1981) definition of brilliance that can be collected from several places of his book: "This quality of returning the maximum amount of light from the stone to the eye - from the surface lustre and from internal reflection - is knows as "life". "The fire of a gem is the display of spectrum colors (and scintillation) caused by its refracting white light before returned to the eye". "Brilliance has never been exactly defined. As it is used in a general way, it should cover all the visual properties which have been concentrated, in the two last paragraphs, into the terms "life" and "fire". .....The brilliance of a stone depends upon the optimum combination of its lifre and fire. If the two qualities could be quantified, brilliance would be at maximum when life X fire was at a maximum".

GIA Diamond Dictionary, 3rd edition:

Intensity of the internal and external reflections of white light from the crown of a polished diamond or other gemstone. Hardness, refractive index, reflectivity, polish, luster, and proportions all affect a gemstone's brilliance.

Diamond Grading ABC by V. Pagel-Theisen, 11th edition:

External brilliance - luster, produced by reflection of light on the surface of the facets; Internal brilliance - refraction and total reflection of light on the pavilion facets; Dispersive brilliance - splitting of scattering of light into its spectral colors = the dispersion which evokes the "fire" or "life" in a brilliant; Scintillation brilliance - the "sparkle" of the stone when moved, caused by light reflections of the light source.

Dodson's definition (1978):

A measure of the light that, entering the crown of the stone, is scattered out of the crown facets.

"Professional Jeweler" (July 1998) Light Return/Brilliance :

The amount of light returned to the eye, or brilliance, depends on how well the diamond in question reflects and refracts light. This includes dispersed wavelengths, which are reflected from the internal surfaces of a diamond and returned to the eye.

GIA (G&G Fall 1998):

White light returned through the crown (excluding glare - light directly reflected from the top surface).

Garry Holloway : http://www.diamond-cut.com.au/09_brill.htm

Brilliance is the human perception of diamond brightness. It is the most important feature of a beautiful diamond.

Brilliance is not simply light return, it involves complex issues that include scintillation or contrast with the added variable of human perception. However a diamond with poor light return cannot display optimal beauty.

Discussion

Today diamond appearance is described by gemologists and those in the trade in terms of Brilliance, Scintillation and Fire. These three terms are commonly accepted as completely describing diamond appearance.

Yet a literature review and comparison of trade opinions show the term "Brilliance" is not clearly defined; there is no one generally accepted definition.

Probably about 50 years ago the word "Brilliance" was used as ultimate description of the diamond appearance. At that time it was a synonymous with "Beauty". An evolution occurred that led to the term "life" to be deleted from the commonly used terms and the term "Scintillation" became commonly associated with the effect of a moving diamond. Fire too has become clearly separated as a characteristic of the colored component of Brilliance.

As you can see there are many different definitions for brilliance in a diamond.

At present time there are three different ideas of brilliance:

Diamond beauty (Life) (as 50 years ago);
Diamond beauty minus Scintillation minus Fire;
Light Return (sometimes including external luster or sometimes taking