I just installed a GFCI outlet in my daughter's room, and that circuit is shared with a few other outlets and two closet lights. When I turn on one of the closet lights, the GFCI trips (pressing reset doesn't do anything) and all connected circuits shut off. This continues until I turn off the closet light. Once the closet light is off, I can press reset on the GFCI and everything's back to normal. Turning on the other closet light doesn't cause this problem (the light just comes on).
Does this mean that there's a wiring fault in that closet light? Or would the fault be in the light switch? What should I look for when I open up the switch or light fixture?