The gear position switch tests good when in neutral. The reason why the multimeter fails to measure continuity (resistance actually) when the ignition switch is turned on is because multimeters cannot function in resistance modes while there is voltage present. Resistance & continuity tests must be performed with the ignition switch off, or the battery disconnected (or the circuit under test unplugged/isolated from voltage).

the very first thing you need to do is, get a 12 volt dc test light. start testing the fuses at the fuse block, see if you are getting power through all the fuses, spec the main ignition fuse !. now go to the ignition switch, at the ignition switch plug, ( where the ignition switch plugs into the wire harness ), test to see if you are getting power to there on the wire harness side, if you are ?, then plug the ignition switch back in, start probing the wires leading to switch ( key end ) with key off, you should have power to key on red wire, with key on, you then should have power coming out of key back through some of the wires, most honda's have power coming back out of key switch on black wire, and pink wires. you are looking for power going into switch with key off, and power coming back out with key on. if this atv sits in a barn ?..mice love barns..and they love to chew on wires on atvs !..lol. sooo..this is a task of tracing down the wire harness..from battery..all the way through every inch of the harness..yes..i know this is a huge task ?..but it must be done !. check  all grounds, all connections, reg/rec, stator, speed sensor, everything !. pretty sure that model has a speed sensor ?, with it being a ele shift, it may also have a gear position indicator on the meter ?..i don't remember if it has all 3 on the meter ?. i had a '98 trx450fm yrs ago, it just had the speed sensor, no gear showing on meter that i recall ?.

you having trouble with that same 500 again ?..man..toss that 500 in the Mississippi river..lol.

you are doing just fine :-).

i work on motorcycle engines as well, too tell you the truth, not much difference between a atv engine, and a motorcycle engine !. what is the problem with your crf 250 big wheel ?. start a thread in the motorcycle thread section, i'll see how i can help you.