Hello, my name is***** to Justanswer! Give me just a few minutes to look up some specifics, I'm working on this now.
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Ok, what type of plastic connector are you working with? Is it a molex connector? Click here to see one of those if you're not sure.
The problem with the plastic connectors is, when they heat up from being used, the pins tend to spread out. I don't think contact cleaner is what you need, but Deoxit is the stuff we use these days. Check the individual pins, and make sure they each make good contact. It sounds like that's exactly where the problem is, it's a loose contact. Since you shimmed it and it worked, the hiccup was caused by vibration, and a connector came loose briefly. Those pins should fit together snug.
Yes, but I would buy it at Best Buy, or Frys, Radio Shack will price gouge you.
Those are the types of connectors that spread out. You can use needle nose pliers to pinch the female ends closer together. Deoxit won't save you from a spread pin. Be careful that you don't pinch it too far, but you want the connection to be tight. If you accidentally pinch it too far, use the end of the pliers to spread them slightly, just enough so the male pin will spread it the rest of the way.
Those connectors need maintenance, and there's even a special tool just for fixing those things. They are poorly designed, and widely used. I'm convinced that is where the problem is.