This problem is very common in gm vehicles. The connector and or bulb contacts may be burnt, just look at the inside of the connector by removing the headlight to gain access. Then reach down and twist the connector out of the signal housing. Remove the bulb and inspect the contacts. If they are pitted and black and white, and the plastic is melted on the bulb, then look inside the connector, it might be burnt too. You can get a new one from gm for about 30- 60 bucks. This problem can be intermittent. hit a bump and it works hit another one and it goes out. Obviously you've already checked that the bulb is not burnt out.