In Fahrenheit 451, did Beatty want Montag to kill him ?
It is suggested that Beatty wanted to die; however, it is also possible to argue that he did not, and because the text is ambiguous, we cannot know for certain.
Beatty is introduced to us as a representative of government power, via his position as Montag's boss and a keenly perceptive and dangerous executor of his duties. We gradually learn more about Beatty, and he becomes more of a dark counterpart or "evil twin" to Montag. He has not only been through the doubts and existential crisis that Montag is experiencing, but he emerged hungry for the simple pleasures that society offers, in order to ward off the dead-end of emptiness that he found in contemplating the universe. He is also well-read, but finds the destruction of books to be a worthwhile price to pay for the stability of society, despite this compromising his morality. In essence, he is who Montag could become, should he fail to see his actions through to their conclusions.
Beatty's actual death is ambivalent; his failing to stop Montag could be perceived either as a quietly satisfied ending to his suffering, or as calling Montag's bluff and losing. Likewise, the twitching of Beatty's eye could simply be the expression of Beatty's inner conflict; the human body wants to live, but Beatty does not. Ultimately the only clear statement on Beatty's intention actually comes from Montag himself:
Beatty wanted to die.
In the middle of the crying Montag knew it for the truth. Beatty had wanted to die.
This is not a clear answer to our initial question, because it is an exploration of Montag's thoughts, not the statement of an omnipotent narrator or a piece of empirical evidence. This could very easily be Montag justifying Beatty's death to himself. The aftermath of the murder clearly hits Montag hard, and he may be doing everything he can to keep functioning, particularly since his own life is still at stake.
Thus, we can say that, while the text says that Beatty wanted to die, it is not necessarily a fact that he did.