The transmission and OD has an interlocking mechanism to prevent reverse from being selected if the OD is engaged. There could be a couple of things wrong and simulating a false engagement and locking out reverse.
If the solenoid was removed during restoration make sure it has been reinstalled properly so that the ball on the end of the solenoid actuating plunger is positioned in the slot in the pawl. It takes a bit of manipulation to extend the plunger and work the ball end into the slot. If it was not engaged properly, the plunger pushing at the end of the pawl could be forcing the pawl in far enough to simulate engagement.
Make sure there is not an electrical miswire so that the solenoid has been activated even though the car is standing still.
Make sure the lockout cable can move the lever to full travel. When knob is pulled out, the end of the lever on side of OD should be forward and almost to its stop. With knob pushed in the lever is to the rear and while not quite at the stop, it is well past straight up and down. Sometimes the cable housing separates from the bracket under the dash and when working the knob, it is the entire cable moving and not the lever on the side of the trans. There is also a retainer at the end of the cable housing at the OD so make sure the cable assy is held tight there too.
If the trans and OD was disassembled then there could be an issue with the way parts were put back together and the lockout mechanism is not positioned or working properly.
If you cannot resolve the issue external via linkage or an obvious problem etc there is a Borg Warner published service and training manual available for download in the literature section.
https://www.packardinfo.com/xoops/html/downloads/BW_OD.pdf It is not Packard specific and as far as the electrical diagram is concerned you would need to refer to the 54 Packard wiring diagrams for the correct schematic. The mechanical part and trouble shooting items are applicable to Packard.
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