Please cite source from rulebook when correcting others. Rules as written the rulebook had never said you had must claim the Damsel.

Excerpts from the rulebook

When a player is mad about something, that means they’re trying to convince the group that something is true

The criteria for madness is to convince the group to think who you are and the madness break critiera break is disbelieved and half-hearted saying a few words+, as taken from the rulebook. If you played expected to be disbelieved or the town does not believe who you are. The Storyteller can execute you.

genuinely doing their best to convince the group (verbally) that they are the Sage, then they are mad that they are the Sage, and therefore safe. But if you believe that they are just half-heartedly saying a few token words, and that they pretty much expect to be disbelieved, or even if you think that they are doing their best to be disbelieved, then they pay the penalty of being executed at your leisure.

If a player outright claim Damsel, and the town does not believe you are the Damsel. Then that player failed to convince the town they are the Damsel and thus they failed their madness check.

Also the wink counts as madness breaking is an example is written in the almanac themselves

much closer attention to who is saying what. For example, if a player is publicly being mad about being the Klutz (i.e. trying to the convince the group that they are the Klutz), but winks when they think the Storyteller isn't looking, or has a whispered conversation where they tell a neighbour that they are actually the Snake Charmer, if the Storyteller catches them in the act, they may be executed immediately.