Bill is right on target. I had the exact same issue with my 58 Burb after I swapped out the transmission for an overdrive unit.

Shifting up into 2nd/3rd was easy. Downshifting was the problem. If I didn't have the lever right in the sweet spot "neutral position" I wold jam the linkage and the tranny would be stuck in third. There is a procedure in the shop manual to fine tune the two shifter forks and the pawl in the shifting box. I ended up loosening the adjuster and using some pump pliers to pinch the three pieces into perfect alignment and then tightening the adjuster. Now it shifts like a champ. It doesn't take much to through off the works. The two forks have to be lined up exactly for the pawl to easily shift between gears. If you don't have it just right, when you try to pull it up/down into first you end up grabbing the corner of the 2nd/3rd fork and pulling it down at the same time. That is what jams the trans in 3rd. Its not a hard job, just consult the shop manual. Good luck.

Thanks

Larry