Yes, I see where you’re going with that. I wouldn’t be surprised if there is a phantom voltage when you turn on the key. Looking at the drawing, you have verified that the Start Pushbutton is working when you tested the yellow wire. Also, when you push the Start Pushbutton, you bring power down from fuse F12, through the pre-start relay coil to ground. The relay should energize, close its contact and bring power from F12 down to the solenoid through the purple wire. That’s the power that will pick up the solenoid and crank the motor. The phantom voltage is not relevant.
You can feel the relay clicking to see if it’s operating. If not, then it’s a relay or socket problem. If it is, but the purple wire is not getting battery voltage, then a socket connection or wiring problem with the purple wire. If you just are wanting to bypass the whole deal with a separate path through a separate pushbutton switch, OK. But that’s how it’s supposed to work. Keep in mind that the Start Pushbutton also provides a ground to pin B-C4 of the ECM, also. Good Luck.