My '04 Expedition 4.6l EB (RWD) is doing the same or similar. It makes a think sound after hitting the brakes at low speeds, usually over bumps or uneven terrain, but delayed almost like a relay or actuator engaging... It always "thinks" twice, like something is engaging then disengaging.
I would like to add...
I just put a new Detroit Axle 12 piece front/rear end kit on it about 8 months ago (upper/lower ball joints, steering end links, sway bar links front and rear, etc) and had to tighten the steering links about a week ago due to play in the steering.... Surprisingly they came VERY loose, scary loose.
Also brand new ceramic pads front and rear, new wheels, alignment, coils, plugs, egr, and a bunch of other shit that cost a fortune.