I would be very surprised if the tank itself is leaking. Having drained the tank, any leak in the connections or hoses will also stop, so that is not definitive.
I can't remember exactly what it looks like now, but surely there is only one connection that is near the bottom (the outlet). I would expect the main filler and the breather to be near/at the top. Dry everything very thoroughly, including under the tank if possible. Sprinkle talcum powder on all available surfaces. Refill the tank and try to trace the source of water that way.