I had the same EXACT issue with my 2000 F150 4X4. An auto shop found that the noise was coming from the left (drivers side) rear wheel. They said that the emergency brake hardware needed to be removed and cleaned and lubed. It really slowed the noise down a lot but I still hear it from time to time. I think that I may trying to replace the E brake hardware and see if that works.

 

Well I just finished replacing both parking brake shoes on both sides along with all of the hardware. Total cost of about $45. I will let you know if it fixed the clicking or not.

 

It has been a few days since I completed this repair and it is safe to say that the clicking noise is FINALLY gone! I found it surprising that noise came from the emergency brake shoes and hardware.

 

I searched everywhere with the same symptoms, it's hard to accurately describe noises. My problem ended up being parking brakes, the pads came off the shoes on the left side, they where popping,snapping, cracking inside the rotors. It was rhythmic where I could tell it was the wheel rotation, but not constant. Just the ends of the pads had crumbled, otherwise in tact so the e brake still worked.