The Doctor's Shirt

The Clothier rotates part of his stock with the moon, and this outfit only shows up on one phase, the waning gibbous. If it is not on his list tonight there is nothing to do but let the moon come back around. Sleeping in a bed runs the clock faster than standing around waiting, which is the quickest way to cycle phases without leaving base.

There is no headwear here, only a shirt and pants, so the outfit stops at the neck. The piece that completes it is the Fez, which the Traveling Merchant carries when he feels like it, and its tooltip says exactly what the character it references would say. None of this affects your stats, so it all goes in the social slots over whatever armor you are actually running.

The whole outfit copies the Eleventh Doctor from Doctor Who, down to the hat being an optional extra sold by someone else rather than part of the set proper.