Sounds to me like the switch is AFU
I would pull the switch connector and make some continuity tests. For tests like this, it is better to use a "big" lamp which will put a certain amount of load on the contacts. That is in comparison to an ohmeter, which draws a tiny amount of current, and can be "fooled" by a "somewhat" switch contact.
What I like to use is an old stop / tail light. I actually have an old stop/ tail socket, so I can hook the bulb up several ways......
1---Using the stop wire and the tail wire, this puts the two bulb filaments in series, draws the "least" amount of current
2---Use the tail wire and the socket ground draws somewhat more current
3---Use the stop wire and the socket ground draws more current yet
4---Wire both stop and tail wires together as one, and use socket ground, and so not you have both bulb filaments in parallel to draw "the most" current.
This old socket and bulb is VERY handy for a lot of this kind of "stuff."
You can also use this socket to act as a resistor, when using a 6-10 amp battery charger to charge a tiny trailer brake or bike battery.
ANY.........HOW................
So take your "big" test bulb, making sure everything is safe, and haywire it to battery +, and hook a good solid clip lead to a good ground. So now you have the ground clip in one hand and the bulb socket connection in the other. Touch them together, the bulb should light.
NOW you can use those same two electrical points to hook to the ignition switch
Hook one of these to the large red (battery in) and move the other to each other color, depending on where the key "is."
'OFF' the red should not be continuous to anything else
both "run" and "accessory" the red should be continuous to the large black
In "run" the red should be continuous to "dark blue"
In "start" the red should be continuous to yellow
and red also should be continuous to brown.