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You're missing a ground Brad.
The radio/dash harness is finding ground through the headlight harness, until you apply power, and then the voltage potential is the same on both sides and no current flows.
The radio doesn't pass enough current to illuminate the headlights, but that's where it's going to ground.
In another thread Brad swapped his cluster and his alternator wasn't charging.
It turned out that one of the two big plugs wasn't seated properly.
Because of that, and the fact that he had his whole dash apart, I am making an assumption that somewhere a ground is missing.
Certainly you can understand that if there is +12V on both sides of a circuit no electrons will flow.
This is how the charge light in the cluster works.
EDIT: the proper EVTM for your '96 Bronco might be a great help with these things.
http://www.ebay.com/itm/1996-Bronco-wiring-diagrams-Electrical-Vacuum-Troubleshooting-Manual-EVTM-/111046053762?pt=Motors_Manuals_Literature&hash=item19dadc4f82&vxp=mtr
Nope. Grounds are good. It is the Multi function switch. had sand in it from my sandblasting fiasco. The radio going out I think was the plug in the back of the dash not being fully seated
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