The first question is whether or not the alternator was ever repaired properly. If it was, then the question is, excactly what is failing, and how was it fixed?
First of all, that test lead is a very frightening piece of kit. Discard it before you hurt yourself. The battery connection can potentially carry the full output of the alternator, depending on the state of charge. If you pump 60 amps through that ridiculous pigtail, you will end up with a blob of red hot copper and flaming plastic.
Don't be adding a ground to the alternator, either. The alternator is firmly bolted to the engine, a break in ground there is all but impossible. But if you're concerned, just pick a mounting bolt and polish it up. A ground between the engine and chassis has to be a very heavy duty connection, because it will need to carry the full output of the alternator, so those little crimp connectors would be quite dangerous, even as a test. The chassis ground strap is a heavy braid for a reason.
As to how to test the D+ circuit, that's done for you. If the light goes on when you turn the key and goes out when you start the engine, D+ is working and the alternator is charging. Done and done. If you want to test it "cold", turn the key to the on position without starting, then measure voltage between the small connector and ground. It should measure somewhere between 9-11V, but as long as it's greater than zero, the circuit is working. If you don't have D+ voltage, the alternator will never start charging.
It's not uncommon to see an alternator fry if the charging circuit is intermittent, and then the problem is more likely B+ than ground. If the cabling is removed while the alternator is running, the stator will discharge it's remaining energy in a huge inductive surge. You may find a bad connector or loose cable. What you want to do is to go over the entire circuit, B+ and ground, between battery and alternator. Start by inspecting the condition of the connector at the alternator, then check the battery clamps. If there is a distribution block between the alternator and battery, check that. Check the body ground on the battery negative cable, and the strap between the engine and body. And when I say check, not a visual. Open each connection and buff it up.