You should check the purple wire with something other than a test light as it doesn't have enough draw to show a real problem. A high beam headlamp will draw much more power and isolate if you just have broken wires or poor wire to terminal connection in the purple crank circuit (which will flow 12v no problem, but very low amps). A voltage drop test with a multi-meter from your ignition switch to the starter solenoid can also show if its a bad wire as well. I'd go from battery positive to starter solenoid to check the whole crank circuit and work it down to segments from there i.e starter solenoid to ignition switch, input to output through the ignition switch, ignition switch to battery ect.
As you can jump the solenoid with a screwdriver and it cranks fine that would indicate that the battery supply cable is ok as well as the ground.
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