I would say you are having a problem with the turn signal as on those cars you push back on it to turn on the bright lights. May need replacing.
Rowefast is correct. The multifunction switch (turn signals and high beams) likely needs to be replaced.
Mine is doing the same..... Found this, hope it helps. I will be changing mine this weekend. http://www.instructables.com/id/How-to-change-a-turn-signal- switch-on-04-Pontiac-/
Looking for a Used Grand Prix in your area?
CarGurus has 2,470 nationwide Grand Prix listings starting at $1,900.
Search Pontiac Grand Prix Questions
Pontiac Grand Prix Experts