I really like this— especially the total mundane-ness of the effect. Definitely upvoted, with a few small suggestions:
Whenever SCP-1525-2 decides to remove any article of clothing, they will immediately assume themselves to be fully unclothed.
Is a key description, and a little confusing as it's phrased. Do you mean after they remove it? All their clothes, or one article? Or … while they're removing something?
I also think it would fledge out the weirdness-horror to list at least a few of the layers the first victim was wearing (like, "ten pairs of socks, of various colors). Humorous and awful at the same time.
Edit: Actually, I'd almost think that "upon waking the next day, regardless of what they are wearing" they'll think they are naked, etc— would make more sense. Either that or "upon fastening the watch", as the variation seems unnecessary/doesn't really add creepiness.