Yea, DO NOT pull a battery cable with engine running as an alternator 'test'
This 'test' which was vaild for older cars and those with generators, not alternators, can instantly fry the diodes in the alternator, and if the alternator was making a lot of amperage at the time you pulled the cable, could send brief spikes of high voltage through the system and perhaps fry some electronics components.
YOur loose battery cable that you peel off with engine running, can also be preventing the charging from occurring.
Overall an intentionally loose battery cable when a charging system issue is being chased, is unwise in the extreme.
There is some sorf of fuse between the (+) output stud and the battery (+). It might even be a length of wire called a fusible link. These are supposed to stretch out when they blow and be obvious, but when they are old they do not blow always in this manner. They are usually a smaller diameter length of wire spliced into a thicker wire. The wire inside is usually 4 AWG numbers larger than the wire it is protecting, like 6awg wire will employ about 7 inch length of 10AWG fusible link. They get old, they blow, even if they are not over their rating. Generally they stopped using fusible links early to mid 90's, but who knows with a Ford and what any previous sparky might have done to it.
Also inspect any and all connections on the back of the alternator, look for wires at the connector which could have overheated. Any looseness of any wire contact in the connector body or brittle wire insulation is a red flag. The presence of Dielectric grease in the connector, does not mean all is fine and dandy inside, as so many seem to think. Usually is obscures an obvious burnt or loose contact within sending one on a wild goose chase.