G'day Howard,
You know, the very first thing I had to deal with on my very first BMW (a 3.0S) 17 years ago was misbehaving wipers. Incredibly enough, I have an intermittent bug in the wipers of my CS at the moment.

Sometimes I think the switch does wear inside. I would push it, get the click, and nothing would happen. Then I'd push again, and presto everything is fine.

All my recent hassles have been with the relay, as Merdad mentions. My problem was the opposite to yours - the wipers would just run when I turned the ignition on, and no mucking about with any switches - the wand, the centre console - would make any difference. Once things had warmed up, the wipers would stop. Trouble was, they wouldn't work at all then!

In my (RHD) car the relay (charmingly labelled "Wish-Wasch Intervall" sits above the fusebox on the near-side (left, ie passenger side) of the car. It's quite a solid black box, bigger than the little silver load-shedding ones in the engine bay - I assume it's the only relay for the wipers - it certainly controls the intermittent function. I don't think they were ever intended to be pulled apart & repaired, but I was quoted a price over Aus$60 over $15 years ago - I suppose they'd be over Aus$200 now! If you do get it apart, you might find bits of metallic dust inside that are causing problems. It's a long time since I've seen inside one. They seem like temperamental things - yet I took mine out, shook it around like a cocktail, put it back, and the wipers are behaving in textbook fashion at the moment. But who knows how long that will last?

I hope your problem's not the steering stalk/wand - those are extortionately priced. Good luck

cheers,
Graeme