332 Garden Tractor Regulator Problem

[bpcook]

I hope to get some help with my 332 John Deere Tractor. My battery light came on and the battery went dead on my tractor. The alternator was putting out over 22 volts AC when idling and over 31 volts when running fast. I only had just over 12 volts at the battery so I felt the regulator would be bad. I ordered a new one on ebay and it came yesterday. It seems to be good but my battery light comes on now. I have over 15 volts at the battery, close to 14 volts going to the ignition over 3 volts going to the battery light at the regulator. The faster the motor runs, the higher the voltage to the battery light. If I turn on the tractor lights, the battery light goes out and I have about 0.1 volts going to the light from the regulator.
I really do not understand what the problem could be and why there is voltage going to the battery light from the regulator when it is sending over 15 volts to the battery. Could the regulator be bad?

Thanks