[theapportioner]

This is how I understood what Seth meant by "external influence":

How does someone explain why he or she wants to commit suicide? One has to give an explanation - I want to off myself because _____. To Spinoza, a possible explanation could be "because my son was killed in the Thirty Years War" or "because I have dishonored my family" or even perhaps "because I am already dying of the Plague". It appears that Spinoza held that it was necessarily impossible that one could rationally argue for suicide for purely internally subjective reasons, such as "because I have a sad temperament" or that "my existence makes me unhappy".

I'm guessing that some sort of Cartesian mind/body separation is implied here, and that Spinoza holds the mind to be fundamentally rational and would not want to do irrational things, but that's just a guess.