Do pilots who have color deficient eyesight see light gun signals differently?
It depends on the type and severity of the color deficiency and on the individual. 

When I first applied for a 2nd class medical, I couldn't pass the color test. I took a practical test with an FAA inspector to get a waiver. We walked outside the FSDO office, and he had me identify the color of the lights being directed at me by the tower. Fortunately, I had been warned to have the tower do this for me on a previous day so I wouldn't be surprised. In my case I had to remember that if I saw yellow, that was white. If I saw white, that was green. Red was red.

When I first applied for a 1st class medical, I again had to take a practical test, but this time from an airplane. I noticed that from the airplane, the white of the green signal was more white, and the yellow of the white signal was more yellow.

Whether the difference from the ground test was due to the increased distance or to my individual daily variation I don't know. I have noticed during physicals through the years that my performance on the color test varies greatly.

In my opinion every pilot should have the tower shoot light-gun signals at him during training so that she/he can see how they look.