If you can't see the mounting bolts, they will be under a removable dress cover under the bowl. Look for a hose type large clamp around the center under the bowl or clips/clamps in the back of the column. Remove it and the cover should be removable. You probably have two bolts if it is Thetford or four bolts otherwise.
The water from the built up area under the leak can flow under the linoleum out to its end under the carpet and then surface there.
You just have to get down on your knees and be brave.... :)
