1999 Other Saturn Models dash lights coming on when we hit t

It sounds like a bad or broken ground wire to you tail lights. Let me start by saying I drive a 18 wheeler for a living. The wires for the tail lights on them are exposed to the weather. It's common for a ground wire to rot or brake. What happens then is when You hit the brakes the brake lights try to light up but since there is no ground the light socket finds a way to complete the circuit (causing a short circuit). That would be the wire for the running lights. That's why your dash will light up when not turned on (false ground) and headlights dim when turned on (wire is in hot)