95 Bonneville SSEI dash lights dim when brakes are pressed...

When I press the brakes (only when headlights are off) my dash lights, radio and Climate control all dim, also the fog lights come on if I have the switch on. However, once my headlights come on there are no problems! I can control how much they dim with the dimmer control on the headlight switch but cannot figure out what is causing the lights to dim ONLY when the brakes are pressed! There are no wires that I can see that are possibly being moved or shorted by the brakes and I don't know where else to look!

Any help would be greatly appreciated, thanks!