There have been plenty of people participating in insurrections with such genuine feelings of wanting what they believe is best for the nation that if an alternative, better path had opened, they would have embraced it, even if it rendered their own role null. Of course plenty of times people also just want to replace those in power, stealing it all for themselves.
Perhaps that Jaymar fellow thought the kingdom is doomed if nothing changes. He was working on it in his own way, which didn't necessarily look too good in our, the readers', eyes. But now that he's certain someone as powerful as Yuki wouldn't let the kingdom fall, for his wife's sake, the minister has got nothing to do anything. Who knows.