I traced my clicking noise back to two components -the rod from the brake pedal lever to the booster, and the brake light switch.

I only noticed the noise after I changed my master cylinder and the fluid was very low/unbled.

It's a lot less noisy now.

I don't know how low fluid would contribute to a loose rod/switch, but it seems to affect it.

Try it yourself -put your head on the floorboard and press on the pedal a few times. You can actually see the source of the clicking.