My car shuts off once in a while when in reverse?

I have. A ford f 150 in line v6 1996. It shuts off very few times when reversing to the left or right. Also the lights dim from time to time when I'm at a stop light. I have a new alt and batt only a week old

Best guess on lights is a bad ground cable (possibly positive cable as well) most times fords corrode inside the cables just behind the post. I'm leaning toward an issue with the neutral safety switch on the reverse issue but could be a few other issues as well.