Hey there. Cloak of the Emperor's Agent is physically identical to Shadow's Cloak from the standard Leviathan set. Unlike the other gear pieces, the class items do not have special glowy parts, and differ to the standard version only in the default shader scheme. Because they are physically identical, only the original Shadow's class item is offered for transmog, and if you want to make it look like exactly like a standard Cloak of the Emperor's Agent, you can use the Calus' Treasured shader on it.
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That'd explain it. Thanks!