70 C20 Won't run with battery unhooked

[70C20Longhorn]

I've always understood that an engine should run without a battery. It could be jumped and then run til it's out of fuel. My truck starts and drives but as soon as I unhook the battery it shuts off. I did the external to internal alternator conversion using an alternator from a 1980 K20. Now I checked for power at the alternator (truck not running) key off I have 12 volts and key on 12 volts. As I understand I shouldn't have power at the alternator with the key off. At first I didn't have my dash plugged in but now I do and same results. Some wiring diagrams show a horn relay, not sure if that would have these symptoms if it's not there. Any guesses...