> But to maximize your influence over a longer time period, you should vote for the third party candidate that most closely matches your views.
That might, arguably, resemble truth if the details of the political system itself were guaranteed stable over time and not subject to alteration by the same people who gain power over other policies through electoral victories. But, in the real world, to maximize your influence over a long-time period, you should organize and advocate for both electoral reform and the minor party you most prefer during periods between elections (the former to work to mitigate the perverse effects of the existing system, the second to maximize the likelihood that, in the next election, the competitive major parties -- which can change over time -- will include the party you most prefer.)
But, once its clear who the major candidates are in the present election, you should still generally vote for the one least harmful to your interests if they win.
> If politicians expected voters to vote on principle and to hold them accountable, we'd have an entirely different sort of politicians.
With no changes to the electoral system, what we'd have with that is "major" parties representing even smaller pluralities (well, technically, only the biggest would be a plurality), and more negative campaigning directed by each major candidate at getting voters best served by the other to not vote for them to "hold them accountable" for something. Which is a change of degree, not kind, from what we have now.