The brakes and the brake lights are on different pins on the trailer connector, and just running brake-light current to the braking circuit is likely to get you brief very-jerky brake application followed by a blown fuse in the tow vehicle.
I like having a brake controller, though we towed the Argosy 10 miles or so without one on the day I took possession. For a long, highway run like you describe I'd want trailer brakes, and you're probably legally required to have them in 1 or more states along the route.
I'm happy with the Prodigy P3, personally, though it requires some fiddling to get it right.
Il Carriaggio — 1975 Argosy 24 | Il Progetto — 1976 Argosy 28 Center Bath | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill