I had a '63 C10 and I still have a '62 C10. I have always had the handles oriented in the "downward" direction. Gravity keeps them from locking or unlocking. Push forward locks, pull back unlocks/opens door.
Only suggestion I could make for a temporary fix would be to try that on your truck. Let it be a gravity assist to keep it unlocked. At least until you can rebuild the mechanism with new parts.
