Headlight problem (Help!)

[Corsair]

I'm writing this on my sister's behalf. Her 66's headlights will flicker and even go out suddenly. When it happens the dash lights and everything go with it but there's no effect on the ignition. She says that they come back on (sometimes)when she accelerates (I"m guessing from the g-force rather than increase in electrical currrent). My Dad thinks it's in the dimmer switch. It seems to be isolated to the lighting system. Apperantly, the lights flicker sometimes when the car is totally off! It sounded at first like a bad relay but if I understand it, her car doesn't have relays. It's pretty wierd. Anybody have any ideas?
Thanks

PS I thought "Christine" was a 56' Fury.