Other reasons for Basil’s anachronistic speech
Assuming that Basil is indeed trained as a spy and not without powers of observation, he should have realized by now that the way he speaks Japanese is not normal. (Honestly, he should have realized that even if he had never been to Japan, CEDEF is not cut off from the outside world.)
Therefore, I propose that he continues to make a fool of himself on purpose, potentially for the following reasons:
Spite. He’s actually conducting a social experiment to see just how far he can go with the act before his master fesses up. So far, the conclusion is infinitely far, and that Iemitsu will confess never.
Guilting Iemitsu. Iemitsu might not ever confess to making a fool of his apprentice, but he does sort of feel guilty about it, so Basil has realized that his boss is a whole lost more amiable to his requests if he buckles down on his Ye Olde Japanese.
Playing stupid. Being underestimated is quite useful in his line of work, and people seem to dismiss him as a gullible fool the moment a “thou” passes his lips, at which point they forget that he successfully survived two chases across Eurasia alone. Given how little effort they put into lying to the teenager who believes that Japanese people speak this way, it’s hardly a surprise when they get caught due to the information they let slip to the person they thought was an idiot.
Spite again. Iemitsu is a Japanese man in the rather xenophobic mafia. Emphasising that aspect of his master’s identity reads as rather viciously spiteful. Jury’s out on whether Basil’s trying to make Iemitsu uncomfortable or his detractors.
Leading on this point and my decoy son headcanon, playing up Japanese stereotypes makes it more likely that people actually believe in a degree of family relation between the two, and when you need people to believe that the Young Lion’s hiding his son in plain sight so they don’t need to look further, every little bit helps.
