i had the same happen to me in my 90. i eventually ran my own ground for the radio and eveything worked out fine. all lights and radio worked when everything was on.

 

Hmm, seems logical. I will have to dig out my Volt meter and see if its a faulty ground wire. The truck came with the factory plug already cut off and most of the radio wires for that matter. I will get a better look at the wiring when i rip the dash out. Stupid heater core is dripping coolant everywhere. -_-

 

i just solved a similar problem on my car i bought a Cd/dvd player for my 2000 concord lxi i hooked it up and hooked a rear-view camera and it worked perfect but wen i turned the headlights on the cd player shuts of so i disconnected the orenge wire that came out of my cd player from the orange on the aftermarket harness then grounded the ping wire (rear con wire) it worked fine but i couldn't see any footage from the camera for that i bought a long red power wire and hooked it to the red camera power wire that hooked from camera to reverse light and took the other end of the new wire i bought and hooked it to the orange wire that came out of the cd player now every thing works fine. you probably dont have the right power to run both cd and head lights thats why you need constant power to run both just hook up an extra wire between a positive wire to the orange dimmer wire its simple;

ground to ground (black)
12+ positive to 12+ positive (red)
and an extra wire (usually a red 18 guage wire bought mine at walmart) to the dimmer wire from the back of the cd player (orange)