Update (sort of)
I started unhooking all of the wire connectors on the side opposite the solenoid (cleaning the connectors with contact cleaner and a little flat head screwdriver) and I found that the rectifier/regulator plug was pretty bad. So much so, that a wire broke off the moment I touched it. (See pic). Now, They were slowly breaking off one-by one, so I cleaned with contact cleaner and crimped new connectors on each individual pair so as not to confuse (there were 3 white wires, 1 black and 1 red). I made sure to insulate (electrical tape) each newly paired and connected pair and then insulated the whole bundle. I turned on the ignition and started the bike. She started (I affectionately named her Big Red), and I hooked up my multimeter and gave a little bit of throttle. She was charging. I say 'was' because I should have inspected the condition of the regulator better before firing her up (it looked like something raised from the Titanic). The voltage never got beyond 13.8 volts before the regulator started bellowing 'magic smoke'. I shut her down immediately and surveyed the damage. I turned on the ignition and there was nothing (no Neutral light) Luckily, I looked at the post that was at the beginning of this thread and had the foresight because of it to put an inline fuse in (see pictures earlier in the thread). It popped the 10A fuse that was in it (QUESTION - Should it be a 10A fuse that is ran off the solenoid or something bigger?). After putting a new one back in the neutral light was back on and a VERY quick tap of the start button and the starter actuated. So, I am guessing that the regulator 'gave up the ghost' and at first, only broke/melted the red wire off of the connector before I got it. When I gave good solid connections, it decided to give me a fireworks display. I will be ordering a new regulator online, but I have a question. (also, comments are welcomed).
Is there a place (or individual) who makes a pigtail for the connector that was FUBARed? Something that I can just crimp inline. I would hate to get a new rectifier only to have to chop the end off to mate it to the spade connectors I was forced to put inline.
NOTE - I ended up ordering THIS (see Pic 2). The colors are different (the whites are yellow and the black is green), but the pin out looks the same (It is for a XJ600 and like 70 other bikes) and the connector tab is on the correct side. I just don't know if it is physically the same dimension. I guess we will find out. If so, then I hope this helps someone else. The Rectifier comes tomorrow, but I will wait for the connector to come before I put power to it. I will keep everyone updated.
Thanks in advance.