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To back probe you slide a probe or wire down the back side next to the wire.
You are putting the probe through the seal (7) and make contact with the
pin (1) and that way you don't have to worry about stretching the female contact
or risk shorting the male pin out on some other pin.
One quick easy thing to try is a can of electronic contact cleaner and spray both sides of the plug
so you sure that they are clean.You can then put some dielectric grease on things to keep moisture out.
Also if you find damage there are repair instructions in the PDF that I posted with this.