Have a 65 skylark every once in awhile I shift in to reverse and the starter will try to start and stop any thoughts
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You have steering column wiring issues. Start with checking the wire going from the ignition switch to the starter. It sounds like it's live when it shouldn't be, and it sounds like your neutral safety switch is doing it's job by cutting power to the start when you get to reverse. Anything else acting weird at the same time? Like the fuel gauge or an oil light? The power is bleeding from somewhere, or simply your ignition switch is bad.
Or the harness to the starter is twisted around and when the engine rocks from being put in reverse the wires may be crossing at the solenoid. May be a good time to check your motor mounts too.
