any action that puts the focus on the popover panel (not the button) or a layout object inside the panel will open the popover.
Go to Object (can specify the popover panel by name or a named object inside the panel)
Go to Field (specify a field in the panel as long as the field isn't also located somewhere esle)
Go to next field (Not a good idea as changes to the layout tab order would screw this up, but it works)
Any script step that starts with "Insert" (if it specifies a target field in the popover)
all can open a popover.
And opening a popover trips the onobjectEnter trigger for the popover panel so you could also use go to field or go to object to put the cursor into the popover after the user clicks the popover button. (Or clear can clear the field and put the cursor in place in one go, but again, beware of having two copies of the same field on your layout as can happen if you are using global text fields for temporary input.)
BTW, the above is also true for tab and slide controls. Putting the focus into any object in a given panel of these controls also brings them to the front (and thus into view) and you can give these panels object names just as you can the panel of a popover to use with Go To Object to bring them into view.