Automatic stalls in reverse.

I bought my car from someone who didn't seem to know much. The car would run but stall when going into gear. If you increased the idle you could hold the brake and get it to clunk in and go. The previous owner said an old Mopar guy told him it had a vacuum issue... I was skeptical as well. While tracking down the issue that was the first thing I discovered. After tracking down vacuum, carb linkages, bad electrical connection which were many. I swapped the battery, starter relay, ballast resistor.. I had the transmission and converter Which it really did need as 3rd gear was completely gone and the converter was completely shot. I had a shift kit put in and am happy with the results, but I still had starting and stalling problems which may have been related to this which if someone, including myself and the transmission guy should have picked up as it was wrapped in half a roll of electrical tape.
Even though a bunch of issues may or may not have been a factor I wouldn't go replacing that booster or neutral safety switch just yet and keep looking.

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Being that you pretty much almost exactly summed up my problem I will start looking again. What you pictured above I’m assuming is the NSS? On mine, there is an obvious short on of the three wires, looks melted, it’s also above the engine before it travels down to the tranny. Maybe this wire just isn’t even sending current, or maybe to little. I will clean that up and test.

The previous owner for mine was also very un-knowledgeable. They painted the 360 and 727 blue together, and they also painted the male prongs on the NSS… I have already cleaned that up.