I would suggest this:-
https://www.etrailer.com/Wiring/Curt/56146.html
Instructions are at **broken link removed**
You should connect the stop input to ground, then just connect as you said. Power from battery (via fuse), connect the module wires to the 7 pin wires, and connect your LED lights to the 4 pin socket that comes connected to the module. You might end up cutting off the 4 pin socket and wiring direct.
You could wire that same module to the car's tail lights instead. If your car has separate stop lights, you will need to connect the stop input of the module to them if your extra LED lights are to come on as stop lights as well as turn signals.