Brake pedal Clicking

At the moment I can't get the video to play. This brake system is essentially brake by wire so there is a brake booster pump that often runs which is directly below the master cylinder. This generation has a factory flaw in the system that causes excessive pump cycling. The sound for a failing brake booster is more of a low whirl as the pump raises hydraulic pressure in an accumulator.

 

Sounds more like minor pedal free play than any brake system issue.

 

The two solenoid valves circled in green here are normally open when you are not using the brakes. That open position is their fail-safe position in case the brake computer isn't functioning. In that fail-safe position, the two chambers of the master cylinder act directly to brake the two pairs of wheels.

Whenever you press the brake pedal and the computer is functioning, the first thing it does is switch those two solenoids to the closed position (as shown here). That closes off the two direct fail-safe fluid paths, so the brake computer is in control of fluid to the brakes on the path involving SLA, SLR, and SCC.

That click you hear at the very top of the pedal stroke is those two solenoid valves closing. So it's really two clicks, but simultaneous, so they sound like just one.

(It took me until just last December to finally figure that out, in this post.)