1998 Ford F-150 Brakes

Lets start with what could be a simple solution. Given the combination of observations, inspect the rear brake shoes, (I'm guessing they're drum brakes), to see if one of the linings rusted off or if a problem with the self adjusters has allowed one of them to get out-of-adjustment. Pumping the brake pedal to get it solid is a common sign of rear shoes that have to be pumped out until they contact the drum. You can pump the pedal a second time much faster than the shoes will retract, so the second or third pump makes the shoes move out further than a single pump.

Once you pump the shoes out far enough, when they contact the spinning brake drum, they're going to try to rotate with them, and that can make the clunking noise. The clue is you won't hear it every time, and it's more likely to occur again when you back up and brake.

We also have to consider worn ball joints and control arm bushings, which are a common Ford problem, but inspecting those is best left to the people at a tire and alignment shop. They're experts at finding the causes of noises, vibrations, and bad tire wear.