Select the Popover button and enter True as it's Hide Object When property so that the button is always invisible in browse mode. Put it behind the field so the popover frame will seem to pop out of the field.
Select the popover frame, not the button, and use the Inspector's name box to give the frame an object name.
Use button setup to turn the field into a button that performs this script:
Go to Object ["Put Popover Frame's object name here" ]