Jumping from battery to brown wire bypasses the switch and wiring.
Jumping the green to ground bypasses the regulator.
When jumping the green to ground, you want to watch your battery voltage. It should climb quickly, don't let it go over 15 volts. The TCI box won't like it.
If the connector is getting warm, it's proably a dirty connection inside the plug.
When a connection gets dirty, corroded, loose the resistance through the connection rises, the higher resistance creates heat. The more the resistance, the more the heat.
This bad connection is probably were your voltage drop is from.
If you pull the plug apart and look inside all the metal parts in there should be at least clean, if not bright and shiny.
Spraying a contact cleaner in there will get most of the crud. If not you may have to remove the wire connectors from the plastic plug to do a better job of cleaning.
To remove the wires from the plastic you need a strong wire, I use a heavy paper clip with one end bent out straight.
If you look at the plastic plug, the connectors are in a slot, centered one one side of the slot is a small rectangular spot/ opening, Slide the paper clip into this spot. While pushing the paper clip in, it will release the lock on the connector. It then should slide out the back of the plug.
It may take a bit of wiggling of the paper clip and wire to get it to released.
Then using the contact cleaner and a small wire brush you can really get the metal clean.
After cleaning, on the female half of the connector you can gently squeeze it tighter. reassemble with a bit of dialectric grease to help prevent corrosion and make a better connection.
If they are too bad, Mike's sells replacement connectors and plugs. With them you cut the wire ends off replace with new and install the new connectors in the new plugs and your good to go.
The new wire end crimp on, I would crimp and solder them.
The slip rings on the rotor are the part of the rotor that the brushes touch. The easy way to test the rotor is to remove at least the inside brush. This gives you access to the slip ring. The brushes should be at least 1/4 inch long, 3/8 is better.
Taking the stator off is even better. This gives you room to see the just what your doing. It also makes it pssible to clean the slip rings. Some very fine steel wool or sand paper and your contact cleaner will get them bright and shiny.
The rotor should test out to 5 ohms = or - 10%
If it test out lower it may still charge a bit. It just draws more current. Volts divided by ohms = amps. A rotor at 5 ohms is 2.9 amps. 14.5 volts divided by 5 ohms = 2.9, 14.5 divided by 2.5 ohms = 5.8 amps.
If you do find a bad rotor, get the right puller to pull the rotor, using the wrong puller can damage the rotor. Be sure to take the nut off that holds the rotor on first or you can damage the puller.