That is the ground wire for the wiper motor casing...it actually comes from the blower motor case ground.
You may have a break in that wire somewhere...it should be grounded, and the wiper motor should not be showing any major voltage on the external casing. There may be a small amount that will light up a test light, but it doesn't take more than 1-2 volts to do that.
Can you check it with a meter?
Remember that the wipers work from the
ground side, not the power side...the wiper motor has 12v anytime the key is on. The wiper switch provides the ground, but the motor casing(as well as the wiper switch itself) needs to be grounded also to prevent the smoke from leaving the inside of the wires...

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Joel Adams
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