Is it a Colour or does it also Function?

I'm in the early chapters of a fascinating book on the augmented sixth.  In the past I looked on projects like this with the same sort of bemusement with which I viewed histories of a single year.  Fascinating projects, ultimately revealing in some way -- but, to what end?

The question that's in my mind at the moment is this: how do we describe the augmented sixth in a simple way?

Every university music student is tortured by French, German and Italian sixths at some point in their studies.  They're bewildering, but fascinating.  No understanding of music since the early eighteenth century is complete without some account of these chords.

I have niggling feelings about augmented sixths.  I think this has to do with their double implication, that the members pull in opposing directions.  It's like a rupture in the harmonic tissue.

There's a second question going through my mind, related to the notional history of the chord's origins.  It's clear to see how the augmented sixth arises out of voice leading -- a type of contrapuntal accident, but full of spice.  So, when is it more accurate to describe an augmented sixth as a colour, rather than in purely functional terms?