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Problem seems to be with the headlights heating up and shutting off light a circuit breaker would do. Once the go off they come back on after a few minutes. Being unfamiliar with wiring in this year of truck I am wondering if there is some kind of thermal relay that shuts the lights off if they are burning too hot or pulling to much amperage?
Take the switch out again, and look at the electrical plug. If it looks melted and like it has been hot, it could be causing a bad connection, which is overheating the switch and making it trip out.
Also check out the dimmer switch in the floor. They lead a rough life down there, and sometimes they get corroded and the wiring does not make a good connection.