It probably is the neutral safety switch. With the key on but engine not running, Have someone watch the backup lights and put the shifter in reverse. While they watch the lights, S L O W L Y move the shifter to each side of reverse. See if the lights come on.

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My Truck.. 2007 DODGE, 5.9 Cummins, 6spd stick, 4X4. My car..1977 240D, OTHER WHEELS...1955 VW Oval window bug, European Delivery (Holland) with a 1700cc, 2 barrel, Porsche drum brakes. 1939 WILLYS Pick-up. 1967 Triumph 200cc Tiger Cub. 1976 Honda 550F 4cyl Motor Cycle.