Well, I'd say that comes mostly down to roleplay; I'm not sure that a specific system in-place would be appropriate, especially with how open-ended inspirations can be. I know you're probably looking for a more concrete answer, but I'd say just look at real life. You know someone has a love for their wife or family by observing it, for example.
To give a specific answer, if someone spent a scene trying to figure that out, that'd be appropriate IMO. Obviously, of course, that also depends on the scene and what happens, but assuming the scene was well-spent with their investigating into the enemy, that'd work.
