Open between yellow and ground is a problem. It could be a broken wire/bad connection. What do you get from white to ground? If that is OK and you get battery charging, then you should pull the flywheel and check all the connections.
The lighting windings are grounded. Yellow is at a point at about 85-90% of the total windings, white is 100% of the windings. The reduced output (yellow wire) just makes it easier for a voltage regulator to clip at say 13VAC.
The white wire gives full output so the rectified DC has enough energy to actually charge the battery, say 15VDC. As a test you could connect the white wire to where the yellow wire goes to your lighting and then get some headlight function with the engine idling.
This would indicate that you have a connection problem somewhere regarding the yellow wire. It could be corrosion on the stator connections. If the bike has been hammered hard, the chances are good that water has entered the ignition side of the motor.
I see very few complaints about GG stators. They seem to be very reliable. The AC voltage regulators on the other hand are not so good. Many people with non-estart (AC only) bikes have burned out bulbs. The estart bikes seem to be fine since they use a combined regulator/rectifier unit.
As to your tail light, it could be operating on DC voltage. I don't have a 2013 wiring diagram to check.
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2011 EC250E
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