I assume you've tried some wiggling the bulbs?
Can you elaborate? Did this just start out of the blue or when you were doing something? Is it only the GI on the backbox? Is it at all times, or when you do certain things (like hit the flippers)?
Immediate thought is that this would be something in the games power supply or the wiring to the head, since it is only affecting the backbox GI. Start by checking the fuses (maybe one that powers the lamps is just hanging on by a thread...visually inspect in addition to continuity) and replace as needed. Secondarily, check the power supply board for burnt connectors/pins (and loose wires) running to the head.
After that, you may have to pull out the big guns and test the capacitors, the bridge rectifier and take a look at that massive filter capacitor at the base of the backbox.
Good troubleshooting tutorial for system 3-7 games can be found at http://pinball.flippers.info/system6resources.asp