Why won't my wipers turn off???

I put the wipers to good use for the first time today. They were turning off and then decided not to unless I turned the van off and on again.

It's like they come down, want to stop, but just can't. On one occassion, they didn't turn off right away but eventually stopped on their own a few minutes later.

Also, are they suppossed to have variable speed? Mine seem to, but it's very slight if so. Thx.

Another related question: My windshield leaks right above the mirror where the previous owner ran the gasket but it doesn't quite meet in the middle. Is there a "best" product to stop it? It didn't appear to leak overnight but did when combined with the wind and hard rain going down the interstate.

Laz,
I have the same problem with my wipers a couple of times. I had to pull the fuse to get them to reset them. I think that the switch might be going bad on mine. It could also be your problem if everything is wired up the way it is supposed to be. As for the leaking windshield you can go to an auto body supply & buy a tube of the adhesive that is used to install the side windows in today's vehicles without the window gaskets. It is about the same color as our windshield gaskets so it should blend ok. Just be careful when applying to the area cause it can cause a mess. It is thicker than silicone or any other caulk so it won't be as messy as any of them. I have used it on a couple of old windshield gaskets that leaked & had luck with it.

The wipers have a "park" switch internally so when you turn them off, they don't just stop, but stop at the bottom.
Take a look at the wiring and try to visualize how it works.
It's often a bad ground at the motor, a dirty internal switch or it's just bad.
I don't know what type you have on Chevys, but here is something I found online
http://www.socalvintagechevy.com/Wiper%20Motor.htm