Well, from a quick look on wikipedia it seems most colorblindness is a photoreceptor problem (so problems with the cells on the retina directly).
They do mention problems possible in various areas such as area V4 of the visual cortex (which is tuned for orientation, spatial frequency, and color). It is tuned for "objects of intermediate complexity," simple geometric shapes and stuff. It doesn't handle things like faces or other complex objects.
So colorblindness is most often caused by a problem in the cells of the retina itself (photoreceptors) but can be caused by defects in the parts of the brain that process visual information.
As for testing how the brain maps colors, I do know this.
The brain does associate certain colors with certain emotions / feelings. I don't have the article anymore, but I was reading in a magazine (very old magazine BTW, from the 1980s) about how the human mind assigns emotions to a color. This knowledge is used in many places (here are a few examples):
-- Large bridges like suspension or lift bridges are usually painted blue. For some reason, people committing suicide are less likely to jump off of a bridge painted blue.
-- Ice cream in a red box tends to sell worse than ice cream in a different colored box. (Supposedly this is the case because red is associated with heat, like the ice cream is melting).
-- People's stress levels are generally higher in yellow rooms (yellow is associated with 'hazards' and thus causes increased stress hormone output) As a result, babies tend to cry more in a yellow room.
-- Often, pink rooms are used for interrogation / holding of prisoners (pink has a calming effect)
-- Laundry detergent almost always comes in a blue and orange container because this color combination signifies performance and value (the detergent works well for not a lot of money)
-- Green is associated with 'natural' items (color of trees and stuff like that).
There are others as well, but I can't remember them all. Anyway, a way to determine how the mind perceives colors would be to put people in a certain surrounding (or give them products of certain colors, like the detergent and ice cream examples). See how they react emotionally.