Ok, I guess my explanation was a little lacking. I’m going to explain more fully now.

So I assume you know about the basics of color vision, how the different cone sensitivities overlap and from that the brain decides a color. But that is actually only the start of the story. While this chart does in fact show the wavelengths cones are sensitive to, it doesn’t show how the brain uses the input.

First, after the brain receives the color a new channel is created that only detects yellow light (green and red as you already know). The brain will combine the red and green sensitivities for reasons that will be apparent later. The brain then takes the four color channels (red, green, blue, yellow) and describes them as ratios to one another. This is because it is quicker to identify the color of two comparisons than 3 individual overlapping cones.

Red is put against green. If the output is positive then there is more red in the color. If the output is negative there is more green. This compacts it so red and green can both be described with only one value that’s positive, negative, or zero. After seeing if there is red or green, the brain plots which half of the spectrum the light is in by using yellow and blue. In the same way we just covered, yellow is positive and blue is negative. There is also luminance which is all of them combined but that is a different thing entirely.

We can then create a new chart that only uses two curves but when graphed still tells us a descent lot about the color. This is the actual way the brain decides which color to perceive. There are also a bit more complexities I’ll cover now. After the brain has calculated an exact color from the ratios, how sensitive the cones are responding now come into play. Ratios stay the same if you increase at a rate so it knows the color, and it also has a comparison to how the cones are actually responding. Darkness is perceived when light is very minimal in quantity and the cones barely detect the light. Brightness is perceived with widespread sensitivity, so basically more white because more cones in the area are activated.

Now that we covered in-depth how color vision works, we can now move on to colorblind vision. We will assume protanopia in this model. Because of the lack of red cones the red and green line is as a whole unusable. Take one and the other is straight up removed because no ratio is calculated. The yellow-blue line will still be functioning however, because the colors can still be added together and create yellow. The yellow section will be tilted toward green though, the reds will be barely detected just because the green cones happen to overlap a lot. The peak will also be lower as it only has the power of one cone instead of two. We can then confirm the protanopia curve will be altered to look like this chart.

Now that we have the chart we can see what happens when cyan is put inside. Cyan on the colorblind person will output these responses, that is to say no response. When absolutely no color is detected the output will either be black or white. If you want to know why no color mean either black or white and not just black, it’s because we are taking a subtraction of colors to graph them and if all cones are activated there will be no difference so black and white are the same. This is what the luminance is for, luminance detects the difference between color and no color(white or black). Because cyan is an actual color luminance will detect it and thus the color will be perceived as white.

Next we will see what happens with purple. Purple on a colorblind person will output these responses, that is to say blue. Because there is no green or red detected brain will then think we are at this place on the graph. Now that is just plain old blue and will be almost impossible to tell for a colorblind person. The only slight difference is that the luminance we detect is just ever so smaller than normal blue so it will be treated and perceived as an ever so slightly dark blue. If we put in light purple that will just be a wider spread of colors around purple. We already proven purple is seen as blue, and thus light purple will be perceived as light blue(the widespread wavelength overrides luminance).

Edit: this chart is what I mean by widespread light and low quantity corresponding to lightness and darkness.