I don't know about the pulsing and squeaking when the Brake light is on, but the last time my brake light came on it was just low on fluid. Open the hood and check the brake reservoir to make sure that there is enough fluid in it. Might be just as simple as topping it off.
Worth a shot.
"The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong, it usually turns out to be impossible to get at or repair."
-Douglas Adams, Mostly Harmless