And if the grounds look and feel good, don't stop there.
Follow them along and check the headlight connectors first. Then, and even if you don't think it needs it, I would run a jumper ground wire from the main body tub, or battery directly, straight to the ground wires on the core support.
If not direct to the wires, then at least by creating your own new ground wire to bond the core support to the rest of the system.
In fact, you can even test this theory by simply running a temporary ground wire from the battery negative to the headlight ground.
Oh, and if you have not already (sounds like you haven't) you need to verify that the bulbs are good and the sockets not rusted out.
This is an issue with original Broncos with light problems often as not.
Good luck.
Paul