And by the power vested in me by Gary and the digital age...
This is what a hinge assembly looks like when it is out of the car. It has a centre tube, and the bracket at each end bolts to the sheet metal at the front edge of the hood (which I will show in the next slide). The end brackets MUST rotate freely inside the tube, or the sheet metal on the body will tear.
Here is the same bolt, actually the nut, seen from inside the engine compartment. The headlight cable is just above it, and the drivers side hinge is beside it. I pulled my engine JUST so you could see how the hinge bolts on, so you had better appreciate these photos
And finally, the passenger side nut, seen again from inside the engine compartment. The headlight rod can be seen just in front of the nut, which often obscures your view of it. Typically, when the bracket seizes inside the hinge tube, the body sheet metal tears at the edge, next to the headlight bucket. The best way to repair this is from the FRONT (the first two photos), usually by welding or riveting an angle of sheet metal from the tab that the hinge attaches to, to the edge of the sheet metal the forms the side of the headlight bucket housing.