If you need to reset it, it may have chewed up the small teeth that keeps it in place. You can pry up the arm off of the shaft and then check the teeth. I have taken a small piece of aluminum from a pop can and wedged it in the teeth and arm to make it fit tighter with what teeth were left. Not checking to see that the arms are not frozen stuck before turning on the wipers cause most of this type problem.
If a windshield wiper switch on a 1995 Buick Riviera stays on when in the off position, it might be the fault of the windshield wiper relay. It could also be that the switch itself needs to be taken off and reset on the dial.
Take the cowling off. The wiper linkage should be visible. The linkage has most likely slipped and needs to be put back into place to let the wipers set correctly.
Replace the wiper motor with a NEW one (do not use a rebuilt!)
The non working wiper on the 2001 Century most likely has a broken wiper linkage. The linkage can be checked by removing the vehicles cowling.
In the engine compartment passenger side.
Reset the wiper arm. At the bulkhead end of the arm is a big nut on a tapered shaft. (might be under a cover). Slacken the nut and loosen the arm from the tapered shaft. Move the wiper to a different position on the windshield and tighten the nut. Test wiper to see that blade returns to the new position.
The air went under wiper arms at the back of the hood.
B1245 is Wiper Rear Motor Run Relay Circuit to Battery
Blades are pressed onto posts on the end of the wiper arms. Just pull and wiggle and they'll come off.
The 1999 Buick Century take 22" wiper blades on both sides front. See related link below. Always lookup exact part numbers for the brand of wiper blade you decide to purchase by vehicle make, model and year which ensures not only the correct lengths, but the correct attachments. Not all wipers of a given length fit all wiper arms.
OBVIOUSLY, a cracked or broken wire in the wiring harness is your problem.
The wiper motor bracket has a tab that can bend causing the wipers to park vertical. Either attempt to bend the tab back, or replace the wiper motor bracket itself.