It should run "off the battery". You could have a voltage drop problem in you ignition harness that is causing this. I can visualize a situation, example:
You have a bad connection in either the battery feed through the bulkhead, or the ignition feed coming back out to the ignition system. At very low RPM, the voltage regulator will be feeding full tilt field to the alternator, but it's not turning fast enough to put out. Meanwhile, this is loading down the (bad) connection in the ignition harness, causing ignition voltage to sag.
To check this out, you need to check the drop in the harness from the battery to ignition
You will be checking the path from battery -- starter relay -- fuse link -- bulkhead connector (battery feed red wire) -- to the ammeter -- through ammeter and to ammeter black wire -- to in harness splice -- branch off to ignition switch connector -- through switch -- back out switch connector (on dark blue ignition run wire) -- back out through bulkhead connector -- to ignition system, alternator field, (70/ later) and voltage regulator "I" terminal.
OK take your meter and turn the key to "run" with engine off. If you do not know which is the "key" side of the ballast resistor, check voltage on both sides, and find the HIGHER reading.
Leave this probe connected to the high reading at the ballast, and move the ground probe over to the battery + terminal, or the starter relay battery stud.
What you are HOPING to read is a very low value, the lower the better. If you read MORE than .3V (three tenths of one volt) you do have a drop problem in the harness
Some other issues may be a poor/ bad/ undercharged battery, other harness issues, an alternator that is not outputting what it should, or a much too low idle speed.
What is your idle, "normally" torqflite? In drive?