Assuming your neutral safety switch still works and the car can only be started in park and maybe neutral you can add a second switch on the transmission to handle the reverse lights.
IF the modifications to change to the Packard shift linkage have not destroyed too much of the original GM stub shaft and lever arrangement you may be able to add something like this
Lokar external switch onto the side of the transmission. Remove the two dark green reverse light wires from the original switch and extend them down to the new switch.
If the transmission shaft has been too modified to accept the kit as designed perhaps there is another place where the trigger piece can be installed on the linkage and switch can be mounted differently.
http://www.lokar.com/downloads/pdf-instructions/INS0043-BackupLightNSSwitch.pdfThis Post was from: https://packardinfo.com/xoops/html/modules/newbb/viewtopic.php?post_id=190703