You ask a really important question! I assume the reason that the subject of traffic laws doesn’t appear in classical Jewish writings is because there were no cars until relatively recently. But this doesn’t mean that Judaism doesn’t address this subject.
I asked your questions to a noted Rabbinical authority in Jerusalem. He responded that a person must observe traffic laws for two reasons: One is the Talmudic principle called “Dina d'malchuta dina”, which means “the law of the land prevails.” Secondly, other people (especially children) can learn from your actions, so disobeying the laws could bring others into danger.
These reasons apply both to drivers and pedestrians. For example, it would be forbidden according to Jewish law for a pedestrian to cross on a red light. This is true even when it is clear that no vehicles are approaching since this is the law of the land, and one should also be concerned that others will learn from his behavior and also cross and be possibly put in danger. I personally have seen a person cross the street at a red light, where it was safe for him, but the person on the other side of the street saw this and also started to cross from the other side — without looking — and very nearly got run over by a car driving on the opposite side of the street!
However, the definition of "breaking the law" depends on the way the law is enforced. If the authorities are not so strict, for instance if they won't fine you for going 60 in a 55 mph zone, it would be permitted to go 60. (We don't advocate that you do so; and we're not saying you don't have to pay the fine if you do get fined for doing so!)
I personally am very meticulous about obeying all the traffic laws. For example, when I'm driving down the highway and I pass the sign that says "State Police," I immediately state "Police."
