Sounds more like the switch for those lights fried itself. My headlights did the same thing when I fried the headlight switch, and lemme tell ya, rt. 81 in a driving snowstorm at night with intermitten lights = scary as all hell.
Looking at the wiring diagram in the Haynes manual, I'd say you need to replace the "backup lamp switch" or the "transmission range sensor" which, if I'm reading this diagram right, are attatched to the reverse lights, or "backup lights" by black and pink wires. Where the backup light switch is actually located it doesn't say, but the transmission range sensor is located on the transmission (surprise). I'd advise seeing if you can't ask at a local shop if they know where the backup lamp switch is, or call a Ford Dealership. I think it's most likely the switch, because the transmission range sensor would give you other problems as well if it were going bad, and if you manage to find the switch and take it out, it'll be very obvious if it was causing the problem (it will be corroded, cracked and/or burned). Hope that helps. Good luck.