digital - What *exactly* is white balance?

When setting a white balance configuration, we adjust the temperature and green-magenta shift to a wavelength-intensity distribution of light that correlates most closely with the actual distribution of light emitted from the light source illuminating our scene.

What I don't understand is by what means our camera uses this information to change the way it records the RGB colour data. Assuming that this ideal distribution illuminated our sensor evenly, we would expect white/grey objects to exihibit a particular Red/Green/Blue intensity over the whole of the sensor, and I assume that this pattern would be mapped to equal RGB values in the process of white balance correction. I'm just guessing here though.

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  How exactly is the raw data of the RGB photosites on the sensor converted into pixel RGB values using the white balance modelled distribution of light? If the red, blue and green channels of a little patch on the sensor each collect the same number of photons, then why isn't this represented by a pixel with equal RGB values? Why do we 'correct' this by distorting the values according to the light source?

  
  


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  If the white balance is chosen correctly, won't the light source appear to be pure white? This is at odds with the fact that light sources clearly do not appear pure white in general.

  
  


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  If I want an image not to represent the colours of objects accurately, but to include the colour-casting that my vision is subject to, then what white-balance configuration will achieve this? Is there a sort of global 'neutral' setting which doesn't alter colour casting? For example, white objects do not appear white in a dark room with the red safety light on. I don't want them to appear white in my photos either.

  
  

The two parameters of white balance configuration (temperature and magenta-green shift) alter what the camera thinks is the wavelength-amplitude characteristic of the scene's lighting. How does it use this information (the formulae; what it's aiming for in principle) to alter the luminance of the RGB channels?