Remove the instrument panel from the gas tank and see if you still have the drain. I've seen repro ignition switches that have one or both terminals touch the gas tank when mounted. My repro switch also did this until I bent the terminal to the side.
If you have an original popout switch then I've seen the wire inside the armored cable touch ground due to frayed insulation. But this shouldn't be what's killing the battery because the circuit is open when you push the popout IN to turn off the ignition.
Which switch do you have?