It will only send a ground to the starter relay to energize it when it's in the Start position, not when it's in the On position. Your problem could be a bad ignition switch but it's more likely to be a broken ignition switch actuator pin which is a separate assembly from the ignition switch that sits behind the ignition switch. They do break often enough that I bought a spare to carry with me. This is what I bought...
https://www.amazon.com/gp/product/B004BYX8W8/?tag=wranglerorg-
It will only send a ground to the starter relay to energize it when it's in the Start position, not when it's in the On position. Your problem could be a bad ignition switch but it's more likely to be a broken ignition switch actuator pin which is a separate assembly from the ignition switch that sits behind the ignition switch. They do break often enough that I bought a spare to carry with me. This is what I bought...
https://www.amazon.com/gp/product/B004BYX8W8/?tag=wranglerorg-20
I have pulled the ignition switch and actuator pin and the actuator pin is not broken. I removed the ignition switch and checked for power on the red starter wire on the harness plug and measured 12.7v, then put a jumper wire from the red starter wire to the yellow wire directly below it on the ignition switch harness plug to bypass the ignition switch and remain in the “start” position. Still no ground signal. I also bypassed the clutch safety switch by putting a fuse in fuse slot 20.