If you have the original Inland Muncie shifter it will have a "T" lockout that you have to lift up before moving the shift lever to the left and forward.
Put the transmission in neutral and lift the "T" handle up. If there is no resistance to the "T" lockout handle, there is a little steel cable inside the shifter tube that has broken. That spring loaded cable lifts the lockout pawl on the shifter mechanism allowing the transmission to be shifted into reverse.
The cable kit is cheap, but it's not easy to change.
1965 Impala SS Tahitian Turquoise 427 4 Speed