Classic/Antique Car Repair: 1930 Model A Battery Drain, negative battery cable, trickle charge

Question
I just purchased a 1930 Model A Tudor last month. I have no experience with this vehicle, a leap of faith. A car I have wanted since I was a young kid. Started up the car and took it to church. Came out 3 hours later and the batter was completely dead. Brought the car home. Put a trickle charge on the battery and it didn't charge to full capacity. Noticed my ammeter gauge was discharging at -10 with the ignition off, and no key was in the ignition. I disconnected the battery cables and the ammeter gage moved to 0. The battery  took two days on a 2 amp charge to charge the battery to full capacity. The voltage tested at 6.5 volts. Put the battery cables back on and the negative cable created an arc, indicating current was moving out of the battery. The ammeter gauge immediately moved all the way to the left on discharge. It is closer to -20 this time. After 15 minutes the battery lost 75% capacity getting closer to a full drain. I disconnected the negative battery cable and the ammeter gauge moved back to 0. I just happened to feel the generator which was room temperature. However, the little silver attachment or what I think someone has called a cut-out was extremely hot. The fuse on the starter is fine. A little while later after the battery cable had been removed the cut-out was back to normal room temperature. I did not notice any burnt wiring. What is the best method to check the cut-out or generator for possible replacement? The battery retested at 6.5 volts and has bee recharged at full capacity. Thanks for taking the time to evaluate my question.

Answer
This is an easy one.  Your cut-out is sticking.  A common problem.  Take the top can off and try to get it to function properly.  When stopped, the contact should open.  If it sticks, it is trying to run your gen as a motor.  In the long run, spend about $125 and put on a 6 volt alternator.  I installed one for a friend of mine yesterday.  It will charge even at idle.  The cut out function is built in electronically and you have nothing to worry about.
Have fun with that car.
jack