check the ignition control module.
you don't have a 5.3L in the bronco. If it is indeed an Eddie Bauer then it should be a 5.8L, but other options include 5.0L and 4.9L.
Thick film IV ignition system. Attached to the outside of distributor
When mine was doing that, it was the ignition module. Does it start back up after sitting for awhile?
there might two one is under the dash and the other is on the distruber(sp)
http://www.therangerstation.com/tech_library/TFI_Diagnostic.html Heat
1984 ford bronco
Most likely it is the TFI module mounted on the back side of the distributor. Takes a special tool to remove it, available at auto zone for about 5 bucks.
On the back of the distributor which is located on the top of the engine rear center, the ignition module (or TFI module as ford calls it) has two screws bolting it to the distributor and one electrical connection, when you replace this you MUST use di-electric grease when installing the new one or it will fail due to excessive heat created by the engine.
The 1989 Ford Ranger pickup truck ignition module is located on the firewall in the engine compartment. The ignition module will be on the drivers side of the firewall.
You can find the Ford Focus ignition control module beneath the drivers side dashboard. The ignition control module will be above the accelerator pedal.
The 1991 Ford Probe spark ignition module can be found on the firewall in the engine compartment. The ignition module will be on the drivers side of the firewall.