Just to add to CJB's post, and to reiterate on my own earlier post, the fuel
pump and EEC (aka PCM), on the older Bronco IIs, Rangers, full-size and a
few other Ford vehicles, are documented to be troublesome. There is
actually a TSB on the failure of Ranger fuel pump and EEC relays, which
causes the battery to slowly drain overnight (went through this gremlin
myself with my 1991 Ranger). It does not explain in detail what actually
happens, but I would imagine that after numerous years of driving, the
contacts inside the relay slowly wear themselves out to the point where they
eventually 'stick' together, which causes a slow, continous drain on the
battery. In the case of my own truck, both relays are identical, so one
would assume they would naturally fail around the same time.
Good luck and I hope you can figure out what is at fault.