Had the same problem myself. I got a s/h unit from a breaker, it didn't work so he sent another and that didn't work. Then, as you say when I plugged either in the wash & wipers fired up and wouldn't stop. I took one apart as per Bill J's website, ran the motor direct from the battery in both directions and cleaned all the copper contacts. It works perfect now, only difference is when I pull to wash the window it has engaged a timer for the wash jets. Before I got just the timed wipers with wash as long as I pulled the stalk, but now a short pull engages a completely automated process of wash & wipe.
Also, as far as I am aware there are two different headlight wiper versions. Up to '93 and 94-98. My s/h unit was from a '95 and it fitted my '97.