Last question that came up during our game.

One of the players was sent to the brig via a crisis card; as a human, I knew this person was not a cylon, so I wanted to bust 'em out. Can a player visit the brig to instigate the vote there, or is that restricted only to players currently in the brig?

I believe the latter is the case. We played an "executive order" skill card to give the imprisoned player a chance to use the brig action to get out of jail, but otherwise the player in the brig has to wait for their turn to attempt to leave?

Yup, exactly. The Brig and Sick Bay are the only two locations you can't go to on your own will.

You cannot voluntarily move to either the Sickbay or the Brig. See page 8 of the rulebook (section 11).

If you have an executive order, you can grant them actions they need to escape, though.