+1 on Larry's recommendation.
This is actually a common problem where the reveres switch (or bolt) is screwed in too far and doesn't allow the linkage to rotate far enough to select reverse. Remove the bolt and put the car in reverse and then screw in the reverse switch until you just light up the reverse lights (or until you have a closed circuit acorss the switch with a multimeter), then tighten up the switch lock nut and leave well alone.
Good luck,
Julian
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