The 'battery' light is wired into the regulator. Basically, one side of the light is connected to battery power, and the other to the regulator. When the alternator is not generating power, current flows from the battery, through the light, through the regulator and provides enough 'starting power' to get the alternator to start generating.
Once it starts producing power, the alternator/regulator circuit becomes 'self-exciting', with a small amount of power generated by the alternator being fed back to power it.
The voltage across the light then becomes basically zero, as both sides are powered.
If the regulator isn't wired correctly, the light will be on. If that light wire(on the regulator side) ends up shorting to ground, it will also be on.
As much as everyone likes the 3G setup, a 1G setup will work just fine, IF TAKEN CARE OF PROPERLY.
The biggest problem I've seen with the 1G is grounding. There must be a good ground between the regulator case and the alternator(The alternator should be grounded to the battery via the engine block). If the regulator isn't grounded properly, it can easily short out or do other weird stuff.
Run a good heavy wire between the regulator and alternator and it might well fix your problem.
Also, check the connections. On the regulator, you have 4 terminals:
I - Goes to Ignition via the battery light. This terminal CANNOT BE CONNECTED DIRECTLY TO POWER, EVEN SWITCHED POWER. It must go through a light/resistor to switched power.
A - Alternator, should be hooked up to the alternator power terminal, or battery +(usually connected at the starter relay on the fender)
F - Hooks to the F(field) terminal on the alternator.
S - Hooks to the S(Stator) terminal on the alternator.
Check all the wiring and if it's done right, it should work just fine.