Three on the tree is common slang for a 3 speed manual with a column mounted H gate shifter. This goes back to the 1930's at least. I have a 1949 Chevy business coupe and a 1953 Ford pickup with three on the tree. It's a heckuva theft deterrent. The 73-87 three on the tree has a backup lamp switch on the base of the column just like an automatic.
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If I read your post correctly you installed a 3 speed automatic with a 78 automatic column in a truck that had an SM465.
The two backup lamp switch wires should run from inside the cab through the firewall in their own grommet not through the bulkhead plug. You didn't say what year the truck was, just the column, so I can't tell you what the colors are.
The 1978 and 1979 wiring diagrams show a (2973407 Packard 56) female plug on the cab harness optionally plugged into a 2973431 Packard 56 Male Plug that's part of a two wire pigtail running through the firewall for the manual transmission backup lamp switch. You'll probably find this disconnect near the base of the steering column. If so... you can disconnect the manual transmission backup lamp pigtail from the cab harness. Then you can plug the cab harness into the backup lamp switch on the steering column. I'd collect your unused manual trans backup lamp pigtail without cutting it off. Someone going from Auto to Manual might want it.
The clutch starter interlock switch plug (8911921 Packard 56) (usually a Purple and Yellow wire or two Purple wires) should be moved to the Neutral-Safety half of the Neutral-Safety/Backup-Lamp switch. The 1978 and 1979 wiring diagrams show the Clutch Interlock switch has the same plug as the Neutral-Safety switch. I would be willing to bet it will reach if you carefully route the wires up to the column.
The Backup lamp half of the Neutral-Safety/Backup-Lamp switch will show continuity on a meter only with the shifter in the Reverse position. The backup lamp plug terminals should be the ones that are straight inline like this
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The Neutral-Safety half of the Neutral-Safety/Backup-Lamp switch will show continuity on a meter only with the shifter in the Park and Neutral positions. The Neutral Safety terminals should be the ones that are parallel to one another like this
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