I had a 99 Sten and there was nothing I could do to get the headlights off aside from a baseball bat. Taking the relay out will probably keep them on at all times. I disconnected my sensor once and my headlights were on day or night.

Like everyone says, make sure the sensor isn't obstructed. ALSO, re: the running lights going out... It's just the one side right? Happens a lot on Full Size GMs. I heard that you can pay the dealership $40 and they will turn off the running lights permenantly.