Disconnecting the positive terminal of the alternator while running will only tell you that you need to buy a new alternator.. Most alternators require a battery to prevent blowing up the diodes. There is an external diode that can be placed on an alternator, ZAP STOP, I believe that also will protect the diodes should the battery switch disconnect the battery from the alternator. The best way to know what is going on is a current shunt and current monitor/meter, or the cheapest way is an inexpensive voltage meter to monitor the battery voltage. The alternator should output around 14.2 volts to give the battery full charge. There are cheep digital voltage meters that plug into lighter sockets available from auto parts stores....
Cal 9.2 #19 SilverSwan