My Valk is Bleeding Out

[srbarclay]

 It has been cold here, 20's & 30's.
My LEDs had turned on by themselves and drained the battery.
I plugged in the battery tender, because I had unplugged to use the outlet for a power tool.
I started her up the next day and idled it for almost an hour to fully charge up the battery.
 The next day my left rear carb was leaking from the bowl. it was a fast leak.
 I turned the gas rooster off and rinsed off all of the spilled gas.
 What could have caused it and what do I do to fix it?
 Thank you in advance for your replies.

[sandy]

Left rear carb.  Float valve stuck open inside the carb and the fuel valve isn't closing. Pull the vac line off the petcock and see if fuel is leaking there. If so: fuel is going down through the vac line into the intake and leaking out. In any case, pull the spark plug and crank the bike over to blow fuel out the plug hole. DON'T try to start the bike as hydroloc is a very real possibility.

[Chrisj CMA]

The battery needs a full charge on a charger if it really ran all the way down.  If you rely on the alternator to get it back you will be sacrificing 50% of the life of the battery.

[Gryphon Rider]

The battery needs a full charge on a charger if it really ran all the way down.  If you rely on the alternator to get it back you will be sacrificing 50% of the life of the battery.

+1
Idling isn't fast enough to properly charge the battery, and if you bump up the idle speed, you risk overheating and discolouring the headers.  Use your charger.

If your LEDs can turn on by themselves, you need to fix that.