If the lamps are on with the head lights it would be as a marker light. Thee should be a noticeable increase in brightness if the turn signal is activated as they use a second filament with a higher wattage on turn and brake lamps (1157). Not all cars had marker lights, and I don't know if your model did or not. Some came on with anything beyond park on the light switch; while with others the marker lamps went out when the head lamps lit up.
It is just a function of trim level and type of car (make as well as model).
I believe in '64, they still were like the older cars. When you pulled the switch out half way, the Parking Lights came on (along with the Tail Lights) and when the switch was out all the way, the Parking Lights went off when the Head Lights came on.
-Parting Out over 75 '58 to '73 Full Size Chevy Cars-
-National Impala Association
-Vintage Chevrolet Club of America