Dave,
Check the supply outlet fitting carefully to see if it's cracked, or possibly the hose connection to that fitting is leaking...
If the tank is leaking elsewhere...I'd take off that square access plate first in case the drain plug is leaking...
I guess there's always the possibly that the filler connection hose, or it's attachment point could be the culprit - but then I'd think the tank wouldn't leak unless filled up to that level...
If the above are secure and not leaking, yes, you'll have to take off the entire tank cover underneath to gain access to the tank itself and find the problem...
If the tank cover hasn't been 'dinged' by hitting something, I'd think it would be rear for a crack to develop in the tank itself otherwise...
The PO of our AS stuck something when backing up and dinged in the corner of the tank cover - it barely got into the tank, at the top, and our tank actually leads when it's full so I know the crack is at the top of the tank...I've been
putting off the project of removing the cover and trying to fix the tank, as it holds water below 90% full...
Hope you find it's an easy place to repair...