If you read the preceding posts, it is clear that jumping a 12V feed onto the BW wire at the ignition switch (which feeds the solenoid) causes it to spin as expected.
Either the feed to the ignition switch is compromised, or the ignition switch is not working (or wired incorrectly).
Maybe this helps in case you don't have it already (toyota wiring diagram is best in my view).
As you'll see, all pins should be connected together when the key is turned to "Start".
What colour wire does your Black-Yellow connect to at the ignition switch connector on the harness side?
I think this is maybe where the mistake lies
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