That depends on how you want to play it out! Passive rejection of the role will have to be observed -- Frank won't be digging for gold, or hanging out in the Caper barter market, or buying equipment, or talking business in regards to land with any railroad barons, etc. This can all be noted by NPCs, who might at first gently coax Frank into his proper place. Or they might be more aggressive about it.

Active rejection, the sort that would involve Frank rejecting people calling him "Prospector Frank" or "Stinky Frank" if the case may be, or the sort that involves him yelling that everyone was crazy, or sullenly storming off -- that would inspire a more reactive, volatile response. Either way people would notice eventually, lying about your acceptance won't show in your actions, and they will know. Because they'll be watching.

So it's sort of like sensing non-conformity!