when you start the truck does the brake pedal raise or drop at all? maybe an internal leak in the booster. when the truck is running try a stethoscope and listen for air leakage where the pushrod from the pedal goes into the booster. also, when the engine is shut off, the booster should be able to hold a vacuum, enough for one emergency stop application. if you pull the check valve off there should be a whoosh as vacuum is released.
here is a couple of quick reads on testing
https://www.yourmechanic.com/article...-brake-booster
https://www.wikihow.com/Test-a-Brake-Booster