My '97 Ford F-150 truck has power going to the headlights all the time. The back window light is also suffering from the same problem.
It can't be the relay because it clicks when you play with the 2 ground wires by the driver's headlight, and the lights turns off when the ground is disconnected.
I played with the ground while back and it turned off, then when I had to boost the vehicle the lights came back on and stayed on.
P.S. I changed the cab when it started doing this.