This is a common problem in all pre-'92 EFI F-series & Broncos. These Ford-style relays (BROWN socket = EEC power; GREEN socket = fuel pump)are notorious for causing intermittent failures in the EEC & fuel pumps. Yesterday, this EEC PWR relay decided to lock on, killing the battery. Today, its contacts are so bad that the truck won't run. So it's about to be TRASH.
See the NEXT caption.
The brown relay is resting on the vacuum cruise servo, and the yellow connector is for the EEC.
If the Fuel Pump relay comes on with the key and stays ON even when the engine isn't running, read this thread