<VV> electrical mystery

[Tom Berg]

Fellas,
My '64 Monza is dead in the carport, a victim (apparently) of an electrical short. The battery (new a couple of months ago) goes dead overnight; I can jump start it with a booster, and it runs fine and its alternator (not original, of course) seems to charge OK. 
When I turn it off I can restart it soon after. But if I let it sit for a few hours, and especially overnight, the battery (and the car) is dead again. Evidently something is pulling down the battery.
Any thoughts as to the cause? 
--Tom in Ohio