The passengers side weatherstrip was falling apart and allowing rain to drip inside the door. I went to a couple of junkyards but couldn't find any better weatherstrip on the junk vehicles - plus I wasn't really sure how to remove that piece of weatherstrip without destroying it.
Turns out it's really easy once I got the new one and could see how it's fastened to the door. There are four or five metal tabs on a metal piece inside the weatherstrip that slide into slots in the door. Removing it is simple - I sprayed some WD-40 like stuff on it to soften it up and tapped it with big flat bladed screwdriver until it popped out. Installation is simply a matter of positioning the weatherstrip on the door and giving it a few whacks with your hand to seat it into the slots in the door. It slides under the side mirror housing on the front end and the vertical weatherstrip on the back end - so you don't have to remove either of those.
The passengers side beltline weatherstrip is Partslink Number GM1391119 which I purchased from Amazon for $16.78 plus tax (free shipping with Prime). You should verify but I believe that part fits any of the first generation (1983 to 1993) S10's.
Here's a cartoon showing the beltline weatherstrip. The inside is the piece of felt the window slides on and the outside is the rubber drip guard thingamajig that tends to disintegrate over the years. This gives you an idea of the metal tabs on the rubber strip at least.