If the relay clicks, that confirms the switch and relay are both working, and the wiring that triggers the relay is good, so the fault must be somewhere in the switched circuit that the relay triggers. I'll second Geezer's suggestion to check your relevant grounds on that circuit. Then check that you've got 12v to the hot side of the relay, then 12v coming out the other side of the relay when it's triggered, then 12v at the headlight(s).