Yes, depending on the year of the F150, they have fuses for the trailer harness. Brakes and left and right turn signals are all fused. I’ve diagnosed this problem twice on a friends 150 and it’s always been a fuse in the right, (passengers side,) kick panel. Check the owners manual, you’ll find it.
Note, something is causing this fuse to blow. If it’s consistently on the one side of the trailer, you probably have a short in the wire that makes contact with the trailer frame, (common ground,) when you hit bumps or have moisture in/on the frame. If it happens again after replacing the fuse pull the wire(s) and inspect. There is a good chance you’ll find a small area of exposed wire. Just make sure when/if you pull the wire, if in the frame, you carry a return line.
Good luck.