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Depending on model the parking brake is most likely a manual operation of the rear drum brakes. There was at least one high end model that ties in with the drive train.
It could be that your rear drum brakes are worn, which you might not notice all that much with discs on the front. There is also an adjustment that you can tighten assuming that the rear drum brakes are not shot.
Considering the age of the truck my bet would be that the rear drum brakes need attention and that is most likely the root of your problem. My suggestion would be to start there. An inspection would likely tell you much.
When you sort it out please report back to the thread what the problem was and how you solved it . Most of the stopping is done by the front brakes and pads are so easily replaced that the rear brakes wear very slowly. I expect those drum brakes have been replaced maybe once or twice in the history of the truck.