Well, if we interpret "head of government" in the non-literal sense of "whoever is in charge", maybe you could try to have Charles Vyner Brooke have his little adventure in Sarawak and then get involved in dominion politics (Australia or New Zealand)? That'd really be "head of state" in one and "head of government" in another, though. The non-literal definition would probably also be fulfilled many times over by personal unions, so there's that.
Kaiserreich (the Darkest Hour mod) can actually have this, with Nestor Makhno emigrating to France and getting elected on an anarchist platform. Plausibility issues of the scenario aside, it fulfills the criteria. You could probably mirror this in other ways as well - revolutionary leader leads some short-lived revolution before it is crushed, then flees to larger socialist republic and rises to power there. Che Guevara, perhaps? Doesn't even have to be communist - maybe a briefly established republic in Pontus or another Greek-inhabited area by the Greek community, which is then destroyed and its head of government flees to Greece proper - but he gets lots of patriotic cred for his attempt and eventually manages to form a government.
You could also simply have some retired Japanese prime minister be appointed as governor of a puppet state in the Co-Prosperity Sphere, or something like that.
