First, the way the fan works is a little counter-intuitive. When the truck is off (no air pressure), the fan is engaged, by default. When you turn the truck on, the fan clutch switch in the upper radiator tube is a Normally Closed circuit, which turns on a solenoid and allows air pressure to disengage the fan clutch. So it's normal operating state is solenoid powered, clutch pressurized, and fan off. When that coolant switch hits 210 Farenheit, the switch opens, the solenoid shuts off, pressure is removed from the clutch line, and the fan re-engages.
I haven't looked at the wiring diagram (you should, they are in the back of the TMs), but I assume the fording switch is an alternate circuit path to force the solenoid to stay powered, and thus force the fan to stay disengaged. Again, without having seen the wiring diagram, I don't think there would just (alone) be a way to wire the switch backwards, have a faulty switch, etc. that would result in totally opposite behavior (e.g. switch on keeps solenoid off and fan engaged, switch off keeps solenoid on and fan always off). If other components were also wired incorrectly or malfunctioning, you might be able to get other behaviors.
That said, my truck came where someone had taken another one of the overheat warning coolant switches (look the same, but are Normally Open and close at 230 Farenheit) and installed it in the position for the fan clutch switch. The resulting behavior was that the fan would have been always on, and turn off at 230 Farenheit. However, my fan clutch was broken and stuck on anyway, too.