What would cause the wipers not to turn off on a 1992 Chevy WT 1500?

The wiper motor on that vehicle has an internal switch that keeps the wiper after you turn it off, until the wiper blade is in the park position. If that switch has failed, the wiper will continue to run. It's a common failure for older wiper motors and you'll need to replace the motor, but they are available as an after market item so you can purchase one at a local auto parts retailer.