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There is a switch on the transmission that controls the back up lights. First see if it is there. A lot have been taken off. Check to see if the linkage is attached to the reverse arm. I am assuming it is a 4 speed. If it is there look to see if the wiring is there. Two wires a green and pink one should go up into a connecter on the firewall. This then goes inside the cabin. Obviuosly check the bulbs and the sockets. The sockets will sometimes get some rust in them. Also check for good ground wires.
If it is an auto the switch is on the shifter handle. The wire colors are the same pink and green. Check to see if it is there and hooked up.
Yes. The switch will be attached to the shifter. If you connect the pink and green wires the reverse lights should go on. If they do it is in the switch, either bad or needs adjusting. It is on a sliding bracket if I remember correctly.