Since it's a '62, I'll assume it's a slant 6, which has a "pivot rod' type accelerator linkage.
Make sure all the bushings along the rod are lubricated and allowing the rod to pivot freely, likewise with the carb linkage joints. Make sure your throttle return spring is present and providing adequate tension. If an automatic, make sure the kickdown rod is also allowing the throttle to return to idle properly.
BTW, are you sure your floor mats aren't creeping up and jamming the gas pedal a bit?
