Testing a charging system

My Brother in Law's 72 Duster has been at my place since 2007.
He recently said he wants to use it as a fair weather Daily Driver at his place in Phoenix AZ.
He likes these cars but has always had me around to guide everything and advise him. Once he takes the car, he will be on his own.
I'm trying to periodically when time permits, work on this car to ensure that it will be safe and reliable. Today I decided to check the charging system. The gauges are not working, that is on the list of things to do. I suspected that the alternator might not be charging so with the engine running, I removed the negative battery cable. The engine shut down. I should have checked the voltage with my meter but I did not, I just grabbed another alternator from the shed, a nice clean one with a rebuilders tag on it. Once it was up and running, It showed a 13.9 volt reading at the alternator and the battery was at 12.8. I pulled the negative cable and it shut down again. There is a ground cable from the block to the firewall. Why would the engine still stall if the alternator was putting out the right voltage? The battery was just charged. The wiring is all old but seems to work. I have a few Voltmeter gauges I could install.