Also, I happen to test the orange & light/blue wires for the turn signals and they both are lighting up with power even though the handlebar controls/switch is not engaged...
The green wires should be permanently connected to battery minus / frame ground and so always show zero or nearly zero volts when measuring green to battery minus . If and only if the green wiring is not connected to this ground can you expect to see 12V on green wires. Unpredictabel electrical things may happen.
Bottom line is check green to battery ground continuiity.
For testing use a voltmeter. Do NOT just connect green to ground somewhere, this may cause ground loops (multiple connections) or blow fuse/cabling/battery if there is a short circuit hiding somewhere. If you want to connect green to ground but are not sure where the real problem is use a fused wire to be safe untill you are sure.