Writing Python toolbox that gives two options for one parameter?

I use a checkbox and then a conditional statement on the existence of the moveTapToBP variable to achieve a similar logic split.

param2 = arcpy.Parameter(
    displayName = "Move un-snapped taps to their building points",
    name = "moveTapToBP",
    datatype = "GPBoolean",
    parameterType = "Required",
    direction = "Input")
param2.value = False

I got to where I wanted to go using the updateParameters and updateMessages functions:

def updateParameters(self, parameters):
    if parameters[0].altered:
        if parameters[0].value:
            parameters[1].enabled = False
        else:
            parameters[1].enabled = True
    if parameters[1].altered:                
        if parameters[1].value:
            parameters[0].enabled = False
        else:
            parameters[0].enabled = True
return

def updateMessages(self, parameters):
    if not parameters[1].value and not parameters[2].value:
        parameters[1].setErrorMessage(
            '''Either parameter 1 OR parameter 2 must be supplied, but not both.''')
        parameters[2].setErrorMessage(
            '''Either parameter 1 OR parameter 2 must be supplied, but not both.''')
    elif parameters[1].value and parameters[2].value:
        parameters[1].setErrorMessage(
            '''Either parameter 1 OR parameter 2 must be supplied, but not both.''')
        parameters[2].setErrorMessage(
            '''Either parameter 1 OR parameter 2 must be supplied, but not both.''')

return

When the tool loads, the parameters appear as though required, with the green dot:

If both parameters are populated, then it becomes a red error X with the error message:

The updateParameters function disables the other parameter once one parameter is populated.