We just bought a 2001 Limited and have been experiencing the same issue. I have isolated it to the back hatch and spraying it down with WD seems to do it for now. It's nice to see this isn't an isolated problem. Did Ford ever have a TSB on this?
No TSB that I know of, but Ford did start selling a revised door ajar switch. I replaced all 6 of 'em in my old '01, and 2 of 'em were packaged in little cardboard boxes. THOSE boxed units were the old style. The new switches are packaged in plastic bags. BTW, those 2 old style switches did eventually start giving me problems.
FWIW, you have 6 switches on 4 circuits. Each front door has a switch on individual circuits. Each rear door has a switch, but the pair of doors is on one circuit. Finally, you have 2 switches in the rear liftgate, and they're on a single circuit. By far, the liftgate switches are the easiest to replace. WD40 works ... but only for awhile.