This is schematics for my 99 accord v6 but the wire colors I think are the same. Notice 2 ignition wires.

Another thing you can do is spray contact cleaner on the switch. While the ignition harness is diconnected, spray and turn the key to crank and off, back and forth. With volt meter check that you have 12V while you crank. Make sure the 12 volt doesn't dissapear when you wiggle the key. If that doesn't work, you probably need to check the wiring that goes to the switch contacts. Maybe a solder joint or the key contacts itself.