The details of this aspect will vary, depending on the setting and the object of the obsession.
One example: in a modern-day urban fantasy setting, where a policeman suspects that the people he's been investigating are in fact werewolves:
Obsessed with this werewolf thing
There's something supernatural going on, and you're going to get to the bottom of it!
- Remain steadfast in your pursuit of the truth.
- Make you carry on pursuing when you should probably stop… and run!