Whenever possible I define things not based on what goes inside one’s head, but behaviour and words. So for me, “ambition” means a stated goal with success/failure conditions and a time frame.
Just as a silly example: if my TRPG character has the ambition to become the biggest mage of the world, then I’ll have him studying magic when possible, and working his way towards it. The time frame is his whole life, the success condition is to become the top mage, the failure condition is to kick the bucket before that happens.