000819: The tool is not assigned when running a Python toolbox in background geoprocessing

Error Message

After installing the 64-bit Background Geoprocessing Upgrade, and running a Python toolbox in the background, the following error is shown in the results window and the tool fails to run:

"Error 000819: The tool is not assigned."

Cause

A third-party Python module that is referenced in the toolbox is not installed in the 64-bit Python folder for access by background geoprocessing. When the Python toolbox tool is run, 64-bit background geoprocessing cannot access the module in the 32-bit Python folder.

The toolbox appears to be valid with correct syntax because ArcGIS has access to the 32-bit modules, but does not check for the 64-bit modules.

Solution or Workaround

Code:
class Tool(object):
    def __init__(self):
        """Define the tool (tool name is the name of the class)."""
        self.label = "Tool"
        self.description = ""
        self.canRunInBackground = False