Hello MT.IDA, does your dash panel have a small square set of 4 idiot lights? Such as battery, oil pressure, disengage pto, and engage brake? If so, that little box is for the battery light. It is set to turn on the light when voltage drops below a predetermined set point. This has nothing to do with the voltage regulator for the charging system.
I have one on my Craftsman II GT18. I tested the low voltage sensor using a battery and battery charger. Using the wiring diagram for your tractor, and a whole lot of jumpers, connect the low voltage sensor to the battery, and the light to the sensor. The light should illuminate. Turn the charger on for a 2A rate. A DVM would be helpful at this point to see the setpoint. As the voltage rises, it will go above the set point, causing the light to go out. Turn off the charger. Eventually, the voltage will drop and the light will come on again.