my dad's LS was doing this with his tail lights where during night driving, the rear lights would be on as normal and as soon as he hit the brakes a few lights would go dark. we traced this back to several bad grounds on the socket. what i did was pull the wire out that was just pressed against the bulb housing and soldered it directly to the housing this fixed everything. i was lazy and only did only the ones that showed no continuity between the ground wire from the connector to the bulb housing, and the symptoms came back so i had to pull things appart and do the rest.
anyway long story short. you may have a broken ground wire or just plain bad continuity like what i described.