Neither will lock from the inside.
On my '52 (with push button outside opening on one side only) I bought a new push button lock and put it into the handle that needed a lock on the outside. Had a locksmith redo the pins in the new lock mechanism to match the original lock on the other side push button.
I don't remember the details on turn down handles with separate locks (pre-52), but I have a friend that has a '50 GMC with Altman latches. I know he can lock either door from the outside. I can call him for details tomorrow if you'd like me to.
'57 GMC 102, Original 347 V8, HydraMatic, 3.08 rear gear, added A/C, disk front brakes, HEI, AFB carb, '98 Honda Black Currant paint. T-boned and totaled 10/12
'52 GMC 152 Stake Bed, Original 228, SM420, added A/C, HEI, disk front brakes, '67 Chev 3.55 rear gear. Gets used as a real truck.
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