No. of Recommendations: 4
I think the intensity may go down (probably would), but remember that once a group of photons are emitted from the beacon, they travel at c in a straight line. They aren't aware (to my knowledge) of the photons before nor after. If we assume the photons are emitted continuously, and in large numbers nearly simultaneously, they all follow their trajectory towards your wall. Fewer of them would strike any given area on that wall if the beacon is rotating faster, which is why I think we'd see an apparently dimming. But the spot on that wall would appear to be exceeding c, even if nothing in the system we've described is exceeding c.