Replace both the EEC and Fuel pump relays, they are both the same part
numbers. These relays are very problematic on these and the 1/4 ton Fords.
They stick when they go bad and can and will drain the battery overnight. I
went through this last year with my own truck, until I finally took it to a
specialty shop that figured out what the problem was.
For my own truck, there is also a TSB on the internet concerning this
problem, and I think it mentions the full size trucks in the text. Both
relays cost me around $20 a piece. Once you find them, it is a matter of
disconnecting the old relay and plugging in the new one.