I think I figured out how thief didn't have to look to realize what rm was doing.
He simple heard by rm's voice that rm had changed.

(Dexterity + Agility ) / 3 + Girdle of Gender Shift

Or he knew by the fact that it was Red Mage talking about performing services.

Or the fact that it was Red Mage and he hadn't crossdressed for a while.

Or just the fact that it's Red Mage.

You need to have that cosplayer (Be it you or anyone else) perform the Rite of Stat Swap on a scroll of vellum.

The real question you should be asking is why isn't he taking off the hat?

Rm is a kapelophiliac?

Actually, he wears his hat because I had scripted for RM to wander away with the usual "sad face" pose while Thief and Black Mage stared at each other in silent awkward horror. Or, if there wasn't space, we'd just see RM walking away "sad face"-style with only Thief in view.

Turns out I didn't like "sad face" with the dress. It looked kinda stupid. So I skipped that whole bit. But I liked the extra level of weirdness the hat gave the scene, it implied that RM had made a conscious choice to keep it on for reasons beyond anyone, so it stayed.

lol, theif is getting more used to Black Mage, RM gets in touch with his alternate self again, and the reactions of Thief and Black Mage are just brilliant.
I just love it