Headlights, taillights, parking lights, brake lights, and signal lights all lights work independently by themselves fine. But when right turn signal is on and brake is applied the turn signal turns into a constantly on light, and the green turn signal indicator in the dash does the same.The left turn signal does not do this when the brake is applied - only the right one. Also it seems that all lights are brighter when the engine is not running. ????????????????

 

The problem with the right side signal light is easy. When you apply the signal with the brake the electrical system is finding "ground" through the circuits that feed the dash signal and turn signal. Somewhere you have a bad ground for that circuit. It could be as simple as changing out the rear bulb. It may also be the groung connection for the rear tailight is not good. Corrossion, looseness, or disconnected wire is usually the culprit. Also, if you have removed any items like the tail light housing , or some other parts, they may have been part of the ground circuit. Your problem is related to finding a good ground for the circuit completion. Without a good ground, the electrical circuit will find its own ground, by back feeding through idle circuits, such as, filaments in bulbs, or headlamps. Start with the rear bulb, and make sure you have the correct bulb in place. It needs to have the correct amount of filaments to work.