another not charging thread

You timed that well. I just stopped by the computer...
I can confirm the blue field wire is getting voltage, albeit around a volt less than the battery itself, not sure if that is important.
Yes. It means current is flowing through resistance. How much discharge was the ammeter showing?

So, I jumped a wire from the other FLD terminal directly to the negative battery post,
OK. Good to know. Easier to use the engine block or a bracket on the block or heads but what you did should have ensured current flow through the rotor amd back to the battery.

(Reads ~12.5v)
At the alternator output terminal or the battery?

However, I found it interesting that after removing the negative clamp from the battery with the jumper wire still attached to the post, the engine continued to run, so there is charge going somewhere...
Edit: I just realized my previous observation probably just means it's still running off the battery.
When 67Dart273 sees this he's going to yell at you.... not to do that!
edit. Beat me to it!

However since you have done it. It does not mean the engine is running off battery. You were correct in your first thought. When there is no ground connection to battery, the battery can not provide power.
For current to flow it needs a complete circuit.