It depends on the controller. One of mine had no light when hooked up, just a red when the brakes were engaged. The one I have now shows green when connected and turns red when engaged. Consult the manual if you have it or let us know what model it is and someone may be able to help you out.
2012 Chevy Tahoe LTZ - HD tow package
2017 Rockwood 2703WS Emerald Edition