Black duct tape on a light colored hat with Tanglefoot sticky trap adhesive applied. No attractant in it, that’s what your head is for. I’m sure a tape loop works but biting flies are attracted to dark colors so the black tape may work better.
Placing blue Solo cup traps around your property works wonders. Gets buffalo gnats also, they are programmed like deer flies. I put black garbage bags on a couple junk 100lb propane tanks to simulate a dark body and provide some movement and a blue sticky cup head(make sure to tape the bag down or the cup will catch it!). I had to put fresh cups over the first ones within a week they were so loaded. Cups hanging from branches work, not quite as good though. A friend hung a sticky cup from a fiberglass pole on his riding mower and got lots.
Struggle, struggle, die is satisfying to watch when it comes to biting flies.