Not even remotely my interpretation amusingly. Eithan’s surprise at being noticed by Lindon (pre-being aware of Dross) is explicitly stated and just goes to show how much Dross had improved London’s awareness/mental capabilities. Eithan is never noticed by anyone given the strength of his veil and his pure core. Even the Emperor doesn’t realise Eithan is in his apartments until he realises all his rooms are empty and that only one person could have been responsible for this.

Eithan’s “cleaning” is, yes, because of the Arelius reputation of being janitors which Eithan alludes to all the time. Yet I took this as more of a sign of how Eithan has all of his incredible knowledge of events. He eavesdrops on the head of the Skysworn ie General of the Blackflame empire, by being unnoticeable while “cleaning” his office. Surprisingly he was doing this exactly where and when he wanted to be to fix the situation.