I was able to find only one socket so I replaced the one I thought most likely to be the culprit. Now the brake light with the new socket works and the other one doesn't when the headlights are turned on. In fact it is dimmer than before when the brakes are on with the headlights off. Does this make sense? I have another socket on order, be here Monday.
Interesting findings when shopping for a tail light socket. GM only services the tailight harness, $111.82 for each side. NAPA had the socket only with wire pigtails for $24.85. They also have the harness assy for $18.52 per side. So the harness assy which has 3 sockets, wire harness and connector to plug into the main harness is LESS than the socket only and over $93 LESS than GM. ??????
You may find you have the socket connected backwards. The bulb has two filaments, one brighter than the other. Parking light is the dim filament.