The tree of three

I'm thinking you might have things "locked up" due to misadustment, mis-installation, or even the incorrect rods....Stand by....LOL

Just looked over at MyMopar. You'll have to "diddle". They have a service manual for a '60 Dodge seems to be the closest..........or 65 Plymouth

MyMopar - Mopar Forums & Information - Service Manuals

I'd start by unhooking the linkage and with a helper, see if the column part works. You will have to "massage" the levers while someone manipulates the shift lever. These are basically an "H" pattern, if you look down the shift lever as if it were a rifle barrel. Left and Up is "R", left and down is 1st. Both those functions should engage 1 lever in the engine bay with the lever pulled towards the steering wheel and moved up/ down.

With the shifter relaxed towards the dash, the linkage should engage the opposite lever in the bay but will only do so when the two are centered so that the 'gate' allows the column internals to go through the "gate.'

Then with the shifter moved up and down, the opposite lever should move

Generally, the front lever on a transmission is high gear and the next lower, IE 3 and 2. usually, rotating the shaft/ lever CCW from the neutral will engage high gear, and CW should engage 2nd

I don't remember which way the rear shaft works, but same deal, one direction should engage reverse, opposite retation should engage 1st