If the wiper moves with the switch off, one of the wires at the hinge is broken and grounding itself. Not fixing this wire will soon result in other wires getting scored and needing replaceing.
Go to http://www.volvospeed.com/Repair/ and look for an article which addresses this problem. Good site for other proceedures.

Klaus
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(V♂LV♂s 1975 164, 1995 854T, 1998 V70R)

I had a similar problem with my 99. It turned out to be a wire near the upper left hinge that was breaking due to the flexing of opening and closing the tailgate.

The way I was able to diagnose it was by turning on the key and the rear wiper switch, and moving the tailgate through it's travel several times. The motion made the broken ends of the wire temporarily make contact, and the wiper moved partially through it's sweep. That may or may not have any effect on your car. If it does, you know what the problem is. If it doesn't the likelihood of a broken wire is still very high.

Fixing it is another matter. You would need a wiring diagram and a willingness to tear into the big bundle of wires near the left hinge.

Dave,

Based on what you are describing (goes even when the switch is off), I would vote for electrical/switch malfunction.

Find an independent Volvo mechanic and see what they say. Sometimes paying for a diagnosis is better than throwing parts and money at a problem, especially when it is potentially electrical/switch based.

BB
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1998 V 70 BASE