Your stator is a 3 phase "Y" output. The winding "LEGS" are the 3 white wires......call/label them A B C. Look at a parts list to see the stator is a laminated steel ring with a multiple of 3 poles---like 12 or 15. The windings are connected BUT NOT TIED TO GROUND at the starts----thus the schematic Y look. Each leg is wound in series on every 3rd pole and act like stacking a string of batteries in a 5 cell flashlight....except the poles produce AC. The AC output is measured from white to white, white to white, white to white.........A-B, B-C, and C-A. Idle voltage is around 20 VAC leg to leg (3 times). Higher RPM will produce on some systems around 80 VAC.....CAREFULL HERE. The resistance check (here again leg to leg) is thru 2 sets of pole coils.....IN one of the whites----to the center tie point----OUT to the 2 other white wires. Measure A-B, B-C, C-A...... .2 to .3 ohms. Also check for any path to GND....high M ohm scale should be infinite as in open circuit. A 120V/40W light bulb will glow when connected A-B, etc. Some systems will blow the bulb if motor Rs too high
Your problem with the melted connector plug was corrosion. The connection resistance will heat up the terminals and with enough heat, melt the nylon connector body......this goes on for a while THEN it goes BAD when the terminals touch.....shorting out the STATOR windings. If opened up, you will find the varnish burned off 2/3 of the 2 legs effected. The coils short down and the resistance check will be sub .1 ohm. Output voltage test will NOT be equal leg to leg also. As an added bonus, the stator will cook off with additional engine run time.
I found that the voltage REG will still be good.....burned terminals and all.....most of the time......but die later.
The RED wire goes to the + battery terminal. Black goes to GND....- BATTERY POST. Test with a test light to ensure a good connection as in probe to REGULATOR RED wire and clamp to GND AND probe to REGULATOR BLACK wire AND CLAMP TO BATTERY + POST. Voltmeter will lie to you and say a good connection. An example would be BLK test lead to GND......lick finger and touch RED meter lead AND use another finger to touch the + battery terminal.....meter will read 10 to 12 VDC...says you have a good 12V....NOT.
BONUS HINT: finding the correct connector and terminals to match the REGULATOR might be tough. FIX is to use a aftermarket RICK's regulator that has pigtails.......cut and strip both stator and regulator wires.....match R and B......the 3 ph whites don't matter...totally random mix when harness was produced and regulator has 3 identical input circuits.
TEST STATOR FIRST FOR DAMAGE/FAULTS.