Corky, your tail lights are using the bright filament for two things, signal and brakes. The relay combines the two separate switch functions and sends voltage out on *one* wire for each side of the car. See the diagram on pg 14 of Bob's excellent primer:
http://www.erareplicas.com/427man/wiring/wprimer.pdf
Caveat, the schematic does not show the *tail light* or low intensity filament circuit.
Sam