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In 1996 Ranger check fuse #26(10amp) in the cab fuse box, thats for the backup lights, only has 12v with key ON
Wire from that fuse runs to the transmission's Backup light switch
This picture is looking down on your transmission:
https://www.therangerstation.com/Magazine/January2011/M5OD-R1HD/m13.JPG
You see the RED connector, thats the backup light switch, it just screws into the transmission
So if you are under the vehicle on drivers side look up at the top of transmission and you will see this switch
It has a two wire connector
Unplug it
You can put a jumper wire in the connector and then turn key on, backup lights should come on if fuse is OK and wires are OK
If so then plug connector back in and try putting trans in reverse to see if backup lights come on now, key on
If not replace the switch
It could be a problem inside the transmission but very unlikely
People often do their own trailer light wiring..............................
While backup light wire is usually not part of general trailer light wiring, people can damage that wire
Ford uses a Black/pink stripe wire from the transmission switch to the rear of the vehicle inside drivers side frame rail, and then a splice to split that wire to the two bulbs