Newbie in need of rescue.  I bought an '87 Savage that was stored outside for a few years and have had a heck of a time trying to get it running.  I dumped the old gas, flushed the tank and cleaned out the filter.  The carb looks clean, the spark plug is OK, it has a brand new battery. One would think it is ready for a crank-over...
Unfortunately, when the ignition is turned to the "On" position it creates a major voltage drop and drains the battery within minutes.  I have taken all the electrical connections apart and cleaned them up, replaced the starter relay, disconnected the starter, continuity tested all the switches, and replaced the fuses.  Still I get Electron Migration Syndrome!  
Since the fuses don't blow I'm assuming it's not a direct short, but what is left on the bike that could put up such a huge resistance without getting hot enough to make itself known?

You say you put in a new battery? & no smoke?
Was it charged?
Not w/ a car charger I hope?
Do Paladin's thing, if no light, the batt is junk.

You gotta short... haha
Question is, where?
This short has enough resistance not to blow fuses or the battery.
Has the engine been rotated at all?
I'd disconnect the starter and later the voltage rectifier.  Or vice versa.
I'm assuming that the VR directly connects the generator to the battery.  So disconnecting it should disconnect the generator.

These are two major pieces of copper, capable of handling the current neccessary to discharge the battery in short order.  

One week later...

It seems that there was actually two problems.  There was a short in the sidestand relay.  It was a stupid safety subroutine anyway, so I removed it from the electical system.
Then it turned out that the new gel battery was junk as well.  Read as 12.6 volts with a multimeter, but had less than 2 amps when tested at the battery seller.
(2nd) New battery in, useless relay out, and lo and behold--- She started right up!
Now I have to see if I can remember how to ride?

Good catch!
That is the next step before I take it for a ride.  I wanted to get it warmed up first.

OK, new season... same problem.
After getting the bike to start, the weather in Seattle turned bad.  I would go out every other week and start the bike to keep the new battery healthy.  Even on the coldest days, the bike would start right up.  The nice weather came back for a day or two so I went for my first ride.  The bike did great (though I was rusty).
I figured it was safe, now, to plug in the headlight and taillight.
Wrong!
I turned on the ignition switch...
Power [check]
Low Beam [check]
High beam [check]
Horn [check]
Taillight [check]
Brake light [check]

Excellent!  Hit the starter button... click-booszh

Instantaneous battery death!  New battery toast... 12.7 volts, no amperage.
No blown fuse.  No arcing.  No fire.  At least a fire would have been cathartic...!
Now I'm the creative sort, so I turned off the right side of my brain to give more processing power to the left (logical) side.
Please, everyone, examine my reasoning and reply if you detect any flaws (or just tell me to replace the heisenstadt converter and get it over with
To cook a battery instantaneously would require...
a.  Solid connections--- evidenced by No spark, no fire
AND
b.  A large heat sink ---No wires were harmed in the process

The obvious culprit is the starter, it is not on a fuse and contains enough copper to absorb the energy.  Yet, it worked fine for months until the lights were plugged in.
Second best, a short in the lights.  A short in the lighting system would have blown the fuse, and would have done so before hitting the starter button.
That leads me to two equally dissatisfying possibilities:

Coincidence--- There is an intermittent short that just happened to appear at the same time as plugging in the lights.

Overwhelming the battery---  The combined draw of the starter and the headlight/taillight was enough to cook the battery.

I will talk to the battery rep.  maybe there is a fusible link or something in the battery that is going poof.  But why do the failed batteries show 12.7 volts with no amps?

My brain hurts!  Both the left and the right sides!

Bill

I've had a Taiwanese battery which did about the same. I stopped at a petrol station and after filling up it wouldn't do anything. There was 12.8 V or thereabouts and it dropped to under 10V when ignition was turned on and under 2V when starter button was pressed. Ignition off, the battery voltage went back to 12.8V. I had ridden two up with panniers full on a bumpy backroad which may have shaken and broken the battery internally.

First, fix the sidestand safety system. There is no such thing as a "stupid safety subroutine." In any case it wouldn't cause the battery discharge syndrome.

Second, have the battery tested again. The business of starting it up every so often to keep the battery healthy isn't a very good idea - far better is to use a battery charger. You didn't mention what the battery voltage did under load, although 12.7 no-load should be okay. My memory on gel cell batteries is a little rusty, but it seems to me they do better at sustained low-current loads such as standby lighting than on high-current loads such as starters. Believe it or not, there are some applications in which the old standard flooded-cell batteries are superior.