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. Sharky