This problem is on a 2006 GMC Envoy with a 4.2 liter engine. The windshield wipers and washer pump will only turn off when ignition is off.
The first symptom was the washer pump would run constantly. A short time later the wipers also are running. Lower speed settings are the same slow speed. High speed appears to be normal. I am considering replacing the wiper pulse board on the wiper motor. All suggestions are appreciated.

Sounds like a bad pulse board to me. I've heard that *ome GM pulse boards for the wiper motors back then had bad solder joints. Sometimes they do this and sometimes they stop working altogether. I've also heard that sometimes it can be fixed by removing the board and re-soldering the solder points. Otherwise replace it.

Thank you for your response, very much appreciated.

I'd take and solder the pins on the board. Fixes many of them.