You're not doing anything wrong. The cyclic button will not appear because there's nowhere for it to go. You've pivoted the table to display your week/month dimension along the horizontal which means the dimension label is not displayed - this is where the button goes by default.
Annoying as it is, you can achieve exactly what you require using a button/text object (see below).
Here, I'm using the green + button to set the variable vShowAbsoluteRelative. You need to create two PTs in exactly the same location, one with week and one with month as the dimensions and then use conditional show on the PT based on the variable vShowAbsoluteRelative. The value entry is as follows:
=if(vShowAbsoluteRelative = 'Absolute', 'Relative', 'Absolute')
So, when a user presses the button, the variable toggles between absolute/relative and one of the two PTs appears/dissapears. You can hide/show as many objects as you like using this method.