Do political assassins and would be assassins tend to cluster on portions of the political spectrum? Those from the USA in particular, but assuming there isn't enough data, a worldwide answer may be more feasible.
For the sake of the question, suppose that just as an anarchist (or substitute with democrat, republican, etc.) with the flu remains an anarchist... that a mentally ill and violent anarchist remains a kind of anarchist, albeit not a very nice one. Political parties of every stripe disown and condemn supporters who seem crazy or criminal, but such retroactive definitions are incompatible with this question.
Also suppose that just a mentally ill person holding a job as a cook is still cooking decent food, that a mentally ill person working as a political assassin may well be serving saner (albeit immoral and criminal) ends, which place its sponsors somewhere on a political spectrum.
So the sample set is both the John Hinckleys, and the host of unknown James Bonds and their employers.
Note: It might help to view political orientation somewhat more broadly here. Having earlier trailed Jimmy Carter, the crazed Hinckley, (like Paul Schrader's fictitious Travis Bickle), seems quite apolitical so far as textbook two-valued right/left political spectrums go, as does Travis Bickle's non-fiction inspiration Arthur Bremmer. On the other hand, these characters, (real and imaginary), all put an extreme value on political fame, celebrity, and notoriety; it might be argued that some actual politicians do so as well, (i.e. placing the value of their own personal career in politics well above all other values), and are in that sense of the same party.
Speculation: the political orientation in a given system, (i.e. the spectrum), might be much less relevant that the overall instability of the political system as a whole, (the canvas the spectrum is painted on). As with Roman emperors and Henry VIII's wives.