Does your alternator have a DA plug (two wires) on it? If so, try disconnecting the plug and shutting off the engine. That will rule out the alternator if it shuts off with the DA plug disconnected. The sense lead of the voltage regulator is supposed to be connected to the battery but the indicator is supposed to connect to a switched source. If they are backwards the alternator will power the ignition through the regulator and it won't shut off, although if there is a bulb or diode it should prevent that.
Also, some ignition switches (the one on my '50) have two accessory terminals that are isolated, so you can connect the accessories and alternator to one and the ignition to the other and prevent that problem.
