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Bob,how difficult is for you to pull up the center floorboard plate and drive it so you can maybe tell if it is the transmission?I guess the gas pedal may be a problem?
From your description I would suspect the noise is coming from the rear axle. Put the truck up on jack stands and have some one operate it in gear and run it at slow speeds. Apply the brakes lightly to put a load on the rear end try to duplicate the noise.
When up on stands check pinion gear for movement in and out of the housing where drive shaft bolts.
If you drain the fluid, drain it over a magnet to check for metal contamination.
I would suspect you have a pinion bearing issue.
I have a 4 speed non-synchro, and it whines for sure. The distinctive sound can be heard for quite a distance (there's in fact a story Bob Jones and I like to tell about that very thing). If your 3 speed is a non-synchro transmission, and the sound you are hearing isn't something new, I'd say you may not have an issue. The whine could just be part of the charm of driving an authentic old truck and something to be embraced rather than feared.
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