1998 Chevy Cavalier Brake Lights

Its not so much, that the brake lights do not work.
I can actually make them work, but they go right back off.
It has something to do with how the bulb is connected to the contact. I replaced the bulbs, but it still shuts off.
I feel that although the bulbs are connected to the contact, that they may not be connected properly, but its a simple snap in right.
I fix it by pulling on the bulb slightly, as if I'm going to remove it from the contact, and thats when it comes on. I can't get them to remain functioning.
The turn lights blink normally, but flickers fast once the lights are not functioning.

Any advice?