Not really "high speed", but US 45 BYP in Jackson is 55 mph with red lights for most of the highway, and US 45 E to Martin where it's 55 mph bypassing Medina and Bradford has red lights (they enforce said 55 too, at least Bradford is a speed trap, illegal photo speed trap at that, they can't force you to pay the fine since it's illegal, lol). I don't remember the 65 zones having red lights.
US 412 toward Dyersburg and Lexington don't have red lights, US 412 toward Dyersburg AT ALL and US 412 toward Lexington once it becomes 4 lanes until you get into town and it slows down to 40 mph.
I don't remember US 45 W toward Union City since I haven't been on it in a long ass time past Trenton (as in probably when I was 10 or less), plus I don't think it gets past 55 anyway, and I haven't personally driven US 45 south past the South Jackson Walmart, I have been on it down to Tupelo, but a friend was driving, and that was five years ago. I do know it gets up to 65, and I know the 55 zones have red lights though.