I have a similar problem on my 97 z24. Wipers work fine, but when I shut them off, they remain up across the windshield. I took the car to a chevy dealer for a recall and had them look at the wipers. They told me the wiper transmission assembly was bent. I asked how much to fix it and they quoted me $500. The transmission assembly was $290 alone. I laughed at the price. I'm not spending $500 to fix the wipers for a 97 z24. I love Chevy's, but this car was built poorly. Thank god both of my camaro's (96 and 69)were not built this crappy. I've been driving around like that for 10 months now and it really is starting to bother me. I am heading to the junk yard for a used one and will replace it myself when it warms up.
1969 Camaro 350, Trickflow heads, ST-10 4spd, Hotchkis suspension, Baer SS brake kit, moser 12bolt