I would doubt they would use an actual "Projector" for such a projection, so I wouldn't blame you for not seeing it in a walk through. Most likely, they are using a spot light, just like all the other lights, and it has a filter on it with a rainbow painted on this filter.
Now this part is speculation, and I could be wrong: I would think that the "brightness" to the rainbow would be either to the degree of the lightbulbs brightness, OR the strong light could cause the filter to fade and the change this filter every now and then when they go through to change bulbs. I could only imagine a box of rainbow filters sitting somewhere along the catwalk.
Bingo! Your theory is most likely correct! I want to assume the rainbow was added after the Primeval World opened in 1966. I also want to assume the fixture and gobo used was a Source Four (S4) throwing an Apollo Design rainbow gobo.