I've had luck with this:
Your faction comes with a Belief. At any point, you can state that you are doing something because of your belief. If there's some significant drawback that happens to you because of what you do, you'll gain Inspiration. Examples might include: Rejecting healing if you're a Sinker, doing the first bad idea that comes into your head as a Cipher, or giving help to someone who needs it at significant personal cost if you're a Bleaker. The DM is the final judge on whether or not you acting in line with your belief gives you a significant drawback, and note that the drawback must be personal - causing problems for your fellow party members isn't very cash money of you, and your belief isn't an excuse to be a fart.
Anyone can have a belief and gain Inspiration for acting in accordance with it. If you're a member of a Faction, though, you gain an additional benefit: you can spend your Inspiration to use a faction ability. The greater your reputation within your faction, the more powerful abilities you can access.
This makes it:
- something the player can trigger (the player defines their beliefs, and states when their belief is relevant), which is nice because I don't want to keep 5 different motives in my head for every PC's action.
- something I can overrule if there's shenanigans, which is nice because absolutely some of these can be shenanigans if there's no guidelines.
- something that makes the game more interesting, because it requires that the PC suffer some problem to get the Inspiration. There's no benefit to adhering to your belief without cost. Beliefs are only powerful when they are tested.
- something that rewards the player for hosing themselves, encouraging players hosing themselves, which is an important part of the
- something that lets me use the 2e tiered faction abilities, more or less, and ties them to rank within a faction rather than level.