Rain water isnt very conductive and it would take a longgggggggggggg time for it to drain a battery, Rain water mixed with some rust particles is a bit more conductive but still it would take a long time for it to drain one so Id say a short is more likely the cause. If when you remove a battery cable and scratch touch it you see lil sparkies that indicates a current draw but its much safer to remove say the ground cable and scratch touch it to frame (away from near top of battery) to look for sparkies.
If you unhook the ungrounded battery cable and clamp one end of a test lamp lead on the bare battery post then you can use the tip probe end of the test lamp to look for a short as it will lite up if it gets a ground.
If when you shut the tractor off the ammeetr swings to a heavy - discharge the Cutout relay may be stuck closed which will drain a battery veryyyyyyyyy fast plus the genny gets hot. If the belt were removed the genny would actually spin in such a case. However a stuck relay is a very fast battrery drainer as opposed to a minor high resistance short which takes much longer to drain a battery.
The battery itself may be at fault, have a shop load test it maybe. If it still runs down even if you remove a battery cable or ground when shes setting its a battery problem
Give the batery a good cleaning on top and re charge and insure the cutout relay isnt sticking closed and if she still runs down teh test lamp can help find a short