Hello! When this occurs, the Blower Control Module is at fault. The module has battery power applied to it, and when the internal driver/transistor shorts, it applies battery power to the motor at all times.
The fix for this is to replace the Blower Control Module (also called a Fan Speed Processor).
If you would like assistance on how to replace, just let me know!
Thank you for the accept! Under the right hand side of the dash is where the module is located. You may or may not have a hush panel (also called a sound insulator) under the dash. Its a large black cover that covers the underside of the dash. It can be lowered after removing two 7mm screws. (there are actually three screws that hold it on, but the far left screw is hard to get to, and you can make the repair by just lowering the panel instead of completely removing it.
Once under there, and panel (if applicable) removed, you should see this:
Item #2 is the module. It has a three-wire connector going to it, and also a Purple and Black wire coming from it. Unhook the three-wire connector, then follow the Purple/Black leads to theh blower motor and unhook it. Then, remove the two 5.5mm screws that hold the module in place and its out!