1) The thing that Okiya/Akai is covering up is where the latex mask ends and his real skin begins. I haven't bothered to go back through every instance of someone being disguised, but iirc both Araide and Scar Akai always wore shirts with high necks, although in KID's first DC appearance he disguised as Ran in a dress that showed her neck. However, this is assuming that Okiya is disguised using a mask, which is not known for sure, and he did reveal his real eye at the end of the mystery train arc, which I don't think he would be able to do if he were wearing the mask.
2) The thing that is being covered up is not on Okiya's neck, but on Bourbon's. In file 811, Haibara does not yet know who Bourbon is, and still suspects Okiya. It's also been theorized that Bourbon and Haibara's sister have some sort of relationship - http://www.dctp.ws/V78-Reader/V78-7Read/A5.html . Haibara states that she has heard of Bourbon, so it's entirely possible that Akemi told Haibara about some sort of scar that Bourbon has. This is more likely considering that Bourbon met Haibara's parents as well, meaning that Akemi and Bourbon must have known each other from a young age. In addition, in all of his appearances Bourbon is wearing collared shirts:
Spoiler: examples
So, what do you think? In my opinion, it's easier to draw a conclusion from option 1: It would be just another clue that Okiya is Akai in disguise.
For option 2, it's kind of hard to see what it would mean. We already know that Bourbon is Amuro, and the only thing it would do is serve as a defining feature of Bourbon for Haibara, but she already knows who Bourbon is so it would be irrelevant at this point. What else could it signify?
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