After 11 years in New Hampshire, it is likely you have a corroded connection. Take the connections apart and see if you can find the corrosion. After cleaning, it's a good idea to dress the connection surfaces with silicone grease(dielectric grease) to help keep the corrosive environment out of the contacts.
If you suspect brittle insulation on the wiring harness, take the wrap off part of the wiring so you can inspect the insulation. The condition should immediately present itself.
95 E320 Cabriolet, 131K