i think it IS in fact a ground problem, or at least a section of old wire that hasnt been removed yet. I had the same issue with any of my accessories actually. If i turned on the radio, the headlights would dim, and if i pressed the brakes, the radio would shut off. If i had the wipers on, the headlights would dim, and if I hit the brake lights, the wipers would stop (all of this due to the amount of load) but i did alot of rewiring on my alternator and abttery and body grounds, and it has helped, but im still not at the end of the tunnel yet. I hope that helped your situation.