How do I test a furnace limit switch?
grab a multimeter and figure out what the normal operation of the switch is. it's probably 12 or 24 vdc. leave the multimeter hooked up and watch it while the system is off, operating normally, and experiencing the problem. the resistor is probably a supervision resistor, so there are at least 3 possible outputs from the switch: open, resistor load, closed/short.

you can then decide the best way to diagnose the problem.

once you know how it should be operating, you can, for example, remove the switch and short or open or use the resistor to trick the furnace in to thinking it is still hot and the fan needs to keep running. if the fan doesn't run properly, then you know the problem is not the limit switch.