Ok, I like Rusty's extension cord idea.
The real problem is that when the brakes are depressed, the tail lights light up fine, but so do the running lights/blinkers up front... I was told by an friend (who had the same problem on his 67 Chevelle SS) that a bad ground for the brake lights could kick the power to the other (turn signal) filament and send it back to the front, causing them to light up there then ground out. I thought that sounded right, but only one filament lit up in the back when the brakes were depressed, and even after wire brushing a clean ground it still happens.
Ideas?