> What about the right to participate in government?
The right to participate in government can be viewed as the right to be free from government action without you being given the opportunity to participate. It can be met by government not acting, as well as by you having the opportunity to participate (directly or indirectly) in any decision it makes.
I think that those who hold to the pure negative view of human rights absolutely tend to view the right to participate this way (and frequently to prefer government non-action to action-with-participation.)
> And, even with this one, it seems like such a strain to me to say "the right to a fair trial is a negative right because, even though you're compelling the government structures to act in a certain way, it only applies once you're in the justice system".
What I think you miss is that being "in the justice system" isn't something that happens external to actions of the government. So it can be a purely a negative right, in that it requires government not to subject you to the justice system unless in so doing it also acts in a certain way.
If it was conditioned on something outside of the governments control, then it would not be a pure negative right. Particularly, if you view the right to a fair trial as applying not only to conditions when you are subject to the justice system, but to include a right to bring grievances against the government and other members of society and to have them fairly heard by an appropriate tribunal, then it becomes a positive right, because the situations in which it applies are no longer ones that result from government action. But, again, I think that many people, particularly those that view negative rights as the exclusive human rights, view the right to a fair trial in terms that are consistent with the purely negative view (and the right to a speedy trial is, as generally understood in the US, a right of that type, since it applies only to criminal trials, which occur only as the result of positive government action, so it is a right that is a pure restraint on government action.)