Taillights and brake lights are the same bulb, but two different elements and circuits are inside it. You can have one without the other.
Same ground (body) for both. Through The three mounting screws for the taillight housings and that metal plate. Rust anywhere in that path can mess with things. I run a dedicated ground from that plate up into the cabin to the big grounding screw by the parking brake under the dash.
Most common aliment is dirty contacts inside the headlight switch. I just took mine apart today and cleaned and lubed it up.