As advised above, check the harness and connector plug condition first. Put some dielectric grease in the plug once it is clean and verify that all is good using a multimeter. The service manual shows you how to test the gear position switch using a multimeter, in the switches section.
If the wiring, connector plug and gear position switch pass the tests, its likely that the end of the shift drum has broken off. The 2000-2001 Rancher FM/TM models had shift drums which could break and were repaired by Honda for free, but only if/when they broke... there was no blanket recall program for them. That free replacement program has long since expired though, so if yours is broken you'll have to replace the drum yourself with a 2002 or newer shift drum. Ya gotta split the cases to replace that drum.
Let us know what you find.
If the wiring, connector plug and gear position switch pass the tests, its likely that the end of the shift drum has broken off. The 2000-2001 Rancher FM/TM models had shift drums which could break and were repaired by Honda for free, but only if/when they broke... there was no blanket recall program for them. That free replacement program has long since expired though, so if yours is broken you'll have to replace the drum yourself with a 2002 or newer shift drum. Ya gotta split the cases to replace that drum.
Let us know what you find.