Yeah...it will likely be a bit time consuming, but I'm hoping to find whatever the cause of the short is today.  Thanks RT325!

The taillight flashing was likely actually just shutting off or dimming when the signal came on.  Not enough power with battery not working right.

Thanks MarkT.  Well, today's work brought both success and another frustrating setback.  I'm beginning to think this bike is indeed possessed.  I completely disassembled the tail light assembly and the ground wire spade terminal was a corroded disaster.  I cleaned everything and ran 3 completely new wires (blue, yellow and black) and put new bullet connectors (both ends) on all three.  Also put a grommet in the fender where the wires passed though (yes...it was missing.)  Popped in a new fuse....turned on the key and once again, I had all lights working.  Now for the setback...
Just before I was going to quit for the evening, I decided to disconnect the battery and put it on the Battery Tender (I will eventually create "Y" pigtails so I won't have to disconnect it to connect to the Tender in the future).  As I was doing this, I immediately noticed that the red wire off the battery, as well as the main harness that this red wire disappears into...were VERY warm to the touch.  So much so in fact that the electrical tape wrapped around the main harness was starting to get soft and gooey.  My first thought was "what in the hell?" and my second thought was "Why didn't the fuse blow?"  So...I just wanted to double check with you about something, MarkT.  I don't think it would have anything to do with this issue of the heated wire, but when you advised me on connecting the '77 250-D stator wiring to my '75's harness, you said, " You'd connect the single green out of 77 stator to both greens on 75 bike.  Black/white is the points wire, same as your black now. Yellow to yellow."  You don't think this would cause the shorting issue, do you?  The only reason I ask is that when I look at the wiring diagram for my '75, it seems like the green /red wire and green/white wire do the opposite thing within my light switch.  One seems to be for "lights off" and the other for "lights on".  I'm definitely NOT an expert on reading wiring diagrams, so maybe I'm just not understanding this at all...and perhaps this has nothing whatsoever to do with my short/heated wire issue.  If you could assure me of that, I'd greatly appreciate it.  I just don't understand why the fuse didn't blow today though.  I have a 10 amp fuse in the battery's positive wire, which is what the service manual specs show.  Thanks so much for any help you can offer.

Since the fuse didn't blow, it would indicate there is not a direct short, but rather a high resistance short or connection.

To put this in perspective: When the tail light bulb is on, it won't blow the fuse and yet it is so hot that you can't touch it. 
So this means you can have a hot wire without tripping the fuse.

You can put an amp meter in-line with the red wire and measure the current draw. Then start unplugging things until it goes away. Study what you unplugged.

Thank you DEET.  I will give that a try.

My "spidey sense" keeps thinking rectifier on some of these issues but there's no way for me to know and you said you've replaced it and installed correctly.  But just to humor me, try unplugging the rectifier or check if those wires are warm.

Green charges battery.  Rectifier is like a one way valve that only lets + from the stator to the battery. 

Older bikes had "daytime" and "nighttime" battery charging circuits...  hence the two greens.  Early systems had to be more carefully balanced (stator output against electrical load) to keep voltage in check..  Soon after Yamaha started installing voltage regulators, they went to just one charging circuit for both day and night. 

Again, green is on the stator side of rectifier so has no influence on battery powered circuits that are on the other side of rectifier.  Unless you re-engineered the headlight switch with some kind of mods and screwed things up by connecting things there that shouldn't connect?   (You said you fixed the switch I think)

Look at the service manuals.  The 1974 250/360 manual is when Yamaha started really doing nice work with switch legends and clear wiring diagrams compared to the early color coded diagrams.  It's not rocket science. 
 

Thanks MarkT.  I wish it were rocket science; in that...I excel!  When I was a kid, motorcycles and model rockets were pretty much all I was interested in.
You're correct...I did replace the rectifier and installed it the way the old one came out (the way you suggested was the way I installed it).  I'll check it again though.  I have a hell of a time sliding the gas tank back on when I have it off, and there's always a chance that a wire up near the coil got pinched or scraped I suppose.  Any chance the new 2-wire flasher relay could be causing this?  I followed pobit's (the eBay seller) instructions to the "T", which were basically just to install the 2 wires from the old relay to the new one and tape off/don't use the ground. 
No re-engineering of the headlight switch; just a super-glue fix on that plastic slider piece inside and some dielectric grease on the contacts was all I added.
I'm going to try DEET's suggestion and check the current draw on everything being run off the battery and see if I can isolate the problem that way too.  I'll check the wiring diagram for the '74.  I think the diagram I have for my '75 is pretty straight forward too, but I just need to brush up on my electrical circuitry skills I guess.  Thank you again.

Not accidentally got the battery connected straight to the lighting or charging coil somehow in a long roundabout way, so it becomes a resistance but would drag the battery flat pretty quick although maybe not blow a fuse.

With this and some of the other strange issues, that's exactly why I keep suspecting the rectifier...  if it's bad the battery can back feed to the stator.

But apparently rectifier is new and connected correctly.

RT325....I read your latest post here (#78) and I guess I don't really understand it.  Would your theory (if I am in fact understanding it) be that this drain would occur only when the main key switch is on... or at any time that the battery is connected (even when the main key switch is off)?  Thanks.