linkage problem

Probably not
Since you say the shifter was fine before you took it apart;
the problem has got to be in the shifter internal gate,
or the link-rod adjustment.
Those thin plates are gates. Things only work right when the gates are in right, so that big round button can move from one lever to the next.If a gate was not in right, then the button would hang up.
I didn't think it was possible to assemble them flipped.
But maybe it is................................

Got side-tracked with company. Your video shows it all,tho.
Well the shifter didn't go into reverse before I took it apart. That's kinda why I wanted to disassemble it and see what might be wrong. The car did shift into reverse and go through the gears before I took the engine/tranny out.
I cleaned up/painted the engine which seems to run strong, put a new parts kit in the tranny over the winter, and reinstalled the engine/tranny this spring. Replaced the clutch and T/O bearing.
When I put the shifter back in it didn't go into reverse anymore.
I'm willing to purchase a new shifter, but want to be sure it's the problem.
Probably not
Since you say the shifter was fine before you took it apart;
the problem has got to be in the shifter internal gate,
or the link-rod adjustment.
Those thin plates are gates. Things only work right when the gates are in right, so that big round button can move from one lever to the next.If a gate was not in right, then the button would hang up.
I didn't think it was possible to assemble them flipped.
But maybe it is................................

Got side-tracked with company. Your video shows it all,tho.

Figured it out. The slots in the fingers that line up on neutral. The 1-2 and 3-4 slots line up, but the reverse finger has a different kind of slot, that I also lined up with neutral. Made sense to me- why else would they have a slot that would line up with the others? Who knows. The allen wrench even worked with it!
Apparently, that slot doesn't serve any purpose but to confuse someone like myself. So after much wasted time, I put the shifter in a vise, as you suggested, and got the damn thing to shift into reverse. That's when I noticed that the finger itself needs to be lined up with the other two in neutral position. The slot in the reverse finger had nothing to do with the others. Anyway, it's back in and working. Thanks for your help. Maybe someone else can use this bit of info in the future.