Have you checked the slip yoke at the transmission output shaft? If they get dry, they will cause a thumping/popping when starting, stopping, letting off the throttle, etc.

If the truck has a lot of miles it might be the leaf springs are getting weak. When this happens the differential gear box will swing up under throttle. This causes some binding on the drive shaft u-joints. Sometimes something as easy as an extra set of leaf spring straps or helper spring will solve it, but its better to either replace them outright or take them to a leaf spring shop and get them re-arched and clamped.